## Browse

**2020-12-01**

[DOI: 10.21982/m1rv-hq77] ECRVEE: Estimation and Correction of Range-variant Envelope Error in RMA Imagery

Chen, Jianlai; Xing, Mengdao

This is the MATLAB code for the estimation and correction of
range-variant envelope error in RMA imagery. When using the range
migration algorithm (RMA) to performs range cell migration correction
(RCMC) for radar raw data, there will be serious range-variant envelope
errors in the RMA imagery. The purpose of this program is to estimate
this envelope error through the range alignment method in ISAR , and use
the Chirp-Z transform to compensate this envelope error. For the
detailed information about the input, output and parameters of this
code, please refer to the config.m and readme files in the code.

**2020-07-16**

[DOI: 10.21982/44xt-n529] PyOSIF: Optical satellite imagery fusion based on multirresolution approaches

Gonzalo-Martin, Consuelo; Ji, Jiahao; Lillo-Saavedra, Mario; Garcia-Pedrero, Angel

PyOSIF provides a set of Jupiter Notebooks for Pansharpening and fusion
of multispectral-multispectral imagery through multirresolution
algorithms. In particular, three versions of the fusion based on the
Wavelet à-trous Transform are included: the original algorithm, and two
variants that allow the control of the spatial and spectral quality of
the fused image. Other additional codes are included for resizing and
downloading Google Earth Engine (GEE) Data Catalog imagery. The code
allows you to use both GEE images and your own images.

**2020-06-23**

[DOI: 10.21982/pzj2-fm81] Optimized Twin Dictionaries (OTD) for Hyperspectral and Multispectral Image Fusion

Han, Xiaolin; Xue, Jing-Hao; Sun, Weidong

This MATLAB code is designed to fuse low-spatial-resolution
hyperspectral (LH) images and high-spatial-resolution multispectral (HM)
images. The fusion problem is formulated analytically in the framework
of sparse representation, as an optimization of twin spectral-spatial
dictionaries and their corresponding sparse coefficients. More
specifically, the spectral dictionary representing the generalized
spectrums and its spectral sparse coefficients are optimized by
utilizing the observed LH and HM images in the spectral domain; and the
spatial dictionary representing the spatial information and its spatial
sparse coefficients are optimized by modeling the rest of high-frequency
information in the spatial domain.

**2020-01-23**

[DOI: 10.21982/pzc7-1448] Match time series in-situ data with AMSR2 LPRM SM

Ma, Hongliang; Zeng, Jiangyuan

Inputs required are the in-situ time series measurements of soil moisture, which can be downloaded freely from ISMN
(International Soil Moisture Network).

Outputs generated include the AMSR2 LPRM soil moisture series as matched
to the in-situ data.

**2019-11-05**

[DOI: 10.21982/42yk-c774] pycoal

McGibbney, Lewis

Python library for processing hyperspectral imagery from remote sensing
devices such as the Airborne Visible/InfraRed Imaging Spectrometer
(AVIRIS & AVIRISNG). The toolkit provides a suite of algorithms and
CLI for classifying land cover, identifying mines and other geographic
features, and correlating them with environmental data sets.

**2019-08-28**

[DOI: 10.21982/j9jg-vm40] S2sharp

Ulfarsson, Magnus; Palsson, Frosti ; Mura, Mauro Dalla; Sveinsson, Johannes

This code formulates the
sharpening process as a solution to an inverse problem.
It is based on cyclic descent algorithm called S2Sharp
and tunes the parameters using a generalized cross validation
and Bayesian optimization.
This method sharpens the 60m bands B1, B9 and the 20m bands
B4, B5, B6, B7, B8a, B11, B12 to 10m resolution.

**2019-08-17**

[DOI: 10.21982/4vaf-b861] QMOD4

Long, David

This MATLAB code is designed to compute and plot the QuikSCAT version 4
geophysical model function (GMF) used for processing QuikSCAT data into
vector winds. The GMF computes the normalized radar cross-section
(sigma-0) of the ocean’s surface as a function of the 10 m near-surface
neutral-stability wind speed and direction, the radar geometry
(incidence and azimuth angles), and the radar polarization. The code
also illustrates how the GMF is inverted to estimate the wind speed and
direction from multiple collocated sigma-0 measurements taken with
different radar geometries and/or polarizations.

**2019-06-13**

[DOI: 10.21982/2q1x-5x14] Pansharpening Toolbox

Vivone, Gemine; Alparone, Luciano; Chanussot, Jocelyn; Dalla Mura, Mauro; Garzelli, Andrea; Restaino, Rocco

A MATLAB toolbox is made available to the pansharpening community.
Pansharpening aims at fusing a multispectral and a panchromatic image,
featuring the result of the processing with the spectral resolution of
the former and the spatial resolution of the latter. This toolbox
consists of several implementations of pansharpening approaches
belonging to the state-of-the-art of the component substitution and the
multiresolution analysis families. Moreover, the two main protocols for
the quality assessment of pansharpening results, i.e., based on the
full- and reduced-resolution validations, have been implemented. This
software is freely available and can be used for reproducible research.

**2019-05-27**

[DOI: 10.21982/f5pg-p074] skimulator

Gaultier, Lucile

From a Circulation and Wave model, data are interpolated on the sensor
geometry to compute l2a and l2b products. Inputs data must contain at
least coordinates (lon, lat) and ocean surface currents (eastward and
northward components) in netCDF4 format . To compute the error budget
correlated to the current, the following variables are required: mean
square slope (in both direction), significant wave height, wind
(eastward and northward component), stokes drift (eastward and
northward) ice if there is any, rain and sea surface height for nadir
altimeter

**2019-02-12**

[DOI: 10.21982/dpp9-e397] SCoBi

Eroglu, Orhan; Boyd, Dylan; Kurum, Mehmet

SCoBi is a bistatic radar simulator. Inputs are:
1- Transmitter (frequency, range, EIRP, polarization, orientation)
2- Receiver (frequency, range, gain, altitude, polarization, orientation, antenna pattern)
3- Ground (Layer structure, texture, dielectric permittivity model)
4- Configuration (soil moisture, surface roughness)
5- Vegetation (scatterer types and distribution statistics)

**2018-11-13**

[DOI: 10.21982/M8M05W] RelDielConst_Vegetation.m

Ulaby, Fawwaz

Input: Microwave frequency, vegetation moisture content
Output: Real part of dielectric, imaginary part of dielectric

**2018-11-13**

[DOI: 10.21982/M8QP8V] PRISM1_InverseModel.m

Ulaby, Fawwaz; Oh, Yisok; Sarabandi, Kamal

Input: Microwave frequency, incidence angle, polarization, rms height, moisture content.
Output: Radar backscattering coefficient

**2018-11-13**

[DOI: 10.21982/M8VH1Q] RelDielConst_WetSnow.m

Ulaby, Fawwaz; Hallikainen, Martti

The code computes the real and imaginary parts of the dielectric
constant of wet snow at microwave frequencies. Input: frequency and %
wetness, Output: Real part of dielectric, imaging part of dielectric.

**2018-10-01**

[DOI: 10.21982/9k29-dm62] Automatic Morphological Attribute Profiles

Cavallaro, Gabriele

Morphological attribute profiles are multilevel decompositions of
images. This code provides a method for automated selection of
filter parameters to provide representative and non-redundant
threshold decomposition of the image. This is based on
Granulometric Characteristic Functions (GCFs).

**2018-09-05**

[DOI: 10.21982/v18n-hk45] Iterative InSAR Phase Filter

Mestre-Quereda, Alejandro; Lopez-Sanchez, Juan M.; Selva, Jesus; Gonzalez, Pablo

This InSAR Phase filter is based on an iterative method in which the
original phase is progressively denoised with adaptive filtering
windows of varying sizes. The quality of the filtering is
affected by the interferometric coherence, which is related to phase
noise. The power spectrum is used to create a smoothing filter for
the phase that is based on a Chebyshev interpolation scheme.

**2018-08-12**

[DOI: 10.21982/M84W78] FLS Large-Scale Single-Baseline Phase Unwrapping Algorithm

Yu, Hanwen; Lan, Yang

This is the serial C code for the FLS large-scale single-baseline phase
unwrapping algorithm. For the detailed information about the input,
output and parameters of this program, please refer to the yu.cfg and
readme files in the code.

**2019-04-04**

[DOI: 10.21982/vd48-7p51] PyINT: Python&GAMMA based interferometry toolbox

Cao, Yunmeng

Single or time-series of interferograms processing based on python and
GAMMA for all of the present SAR datasets.
1) Sentinel-1: start from data-download to time-series interferograms
2) other: start from SLC datasets to time-series interferograms
Input:
1) S1: tracks, frames, sub-swathes, sub-bursts, start-date, end-date,
subset-area, baseline threshold
2) other SAR data: SLC datasets, start-date, end-date, subset region,
baseline-threshold.
Output:
time-series of coregistrated interferogram files: include coherence,
wrappedIfgram , unwrapIfgram, and geometry file (dem and lookup-table).

**2018-07-09**

[DOI: 10.21982/nkd7-cd05] gapfill

Gerber, Florian

Tools to predict missing values in satellite data and to
develop new gap-fill algorithms. The methods are tailored to
data (images) observed at equally-spaced points in time.
The package is illustrated with MODIS NDVI data.

**2018-04-18**

[DOI: 10.21982/M8192K] GRMDM_O

Muzalevskiy, Konstantin; Fomin, Sergey; Mironov, Valery

The function calculates the complex dielectric permittivity (es) of the
soil with an organic matter content (m0) from 35% to 80% in the range of
soil temperature (Ts) from -30C to +25C at frequency equal to 1.4GHz
(rd is a soil dry bulk density in g/cm^3). To develop the dielectric
model, four soil samples were taken from the Yamal peninsula and the
North Slope of Alaska.

Input parameters: Organic matter content, Soil moisture, Dry bulk
density, Soil temperature.

Output parameter: Complex permittivity

**2018-03-17**

[DOI: 10.21982/M8J91V] Matlab CMOD5 Model Function and Compass Simulation Code

Long, David

Code package includes a Matlab implementation of the CMOD5 geophysical
function relating V-polarization C-band backscatter to wind speed and
direction as a function of incidence angle and antenna beam azimuth
angle, as well as code to implement a simple wind retrieval scheme
to estimate wind from multiple backscatter measurements. A compass
simulation for both the fan-beam and scanning pencil-beam satellite
measurement schemes are included.

**2018-03-17**

[DOI: 10.21982/M8P35J] Matlab NSCAT1 Tabular Model Function Evaluation Code

Long, David

Evaluate and plot tabular NSCAT1 geophysical model function relating
dual-pol Ku-band (14 GHz) backscatter to wind speed and direction for
different incidence angles and antenna azimuth (relative to north).
Directions are specified in oceanographic convention (mass flow)
relative to north.

**2018-03-17**

[DOI: 10.21982/M8XK92] Full SeaWinds Slice Spatial Resolution Function

Long, David

Imaging applications of SeaWinds on QuikSCAT and ADEOS II are
acilitated by applying reconstruction and resolution enhancement
algorithms to produce high resolution images of the surface normalized
radar cross section (sigma-0). Such algorithms require a description of
the spatial response function (SRF) of the measurements. The pencil-beam
design of SeaWinds, coupled with the onboard processing, results in a
spatial response function with varies significantly between measurements
and is a function of orbit and antenna position.
The computational complexity of the SeaWinds spatial response function
requires that a method of parameters for effective use. This code
interpolates two precomputed files to efficiently evaluate a 2d
polynomial parameterized full SRF for individual slice measurements as a
function of orbit position, antenna rotation angle, and polarization.
Fortran, C, and some Matlab versions of the code are available along
with required binary parameter files.

**2018-03-17**

[DOI: 10.21982/M82904] Parameterized ASCAT SZO Spatial Response Function

Long, David; Lindsley, Richard; Anderson, Craig; Figa-Saldaña, Julia

Software for computing BYU's parameterized spatial response function
(SRF) for SZF scatterometer backscatter measurements collected by the
European Space Agency (ESA) Advanced Scatterometer (ASCAT) on Metop
spacecraft series. Includes a test program. Code is written in C but
is designed to able to be used with fortran. The parameterization
enables efficient computation of the SRF function for individual SZO
ASCAT measurements as described and validated in the referenced paper.

**2018-03-17**

[DOI: 10.21982/M8SS5C] CASIE-09 microASAR Processor Demo

Long, David

Matlab code that implements synthetic aperture (SAR) stripmap processing
using the range-Doppler algorithm and spatial-domain backprojection to
create backscatter images. The code includes sample raw LFM-CW SAR data
of sea ice collected in July 2009 by the C-band microASAR as part of the
Characterization of Arctic Sea Ice Experiment 2009 (CASIE-09) conducted
north of Svalbard Island.

**2018-03-17**

[DOI: 10.21982/M8DK9D] Tabularized SeaWinds Spatial Response Function

Long, David

Precise computing the SeaWinds spatial response function (SRF) is
complicated and requires significant computation detailed knowledge of
the orbit geometry and instrument processing. This code computes an
approximate SRF for SeaWinds based on precomputed tables. The SRF is
computed as a function orbit position, antenna rotation angle, and
polarization. The full footprint "egg" SRF is approximated by a 2d
polynomial while the "slice" SRF is approximated by a shaped boxcar.
Details are given in the referenced paper.

**2018-03-08**

[DOI: 10.21982/M89S51] TSPA Multi-baseline Phase Unwrapping Method

Lan, Yang; Yu, Hanwen

This is the serial MATLAB code for the TSPA multi-baseline phase
unwrapping method.There are three unwrapping models can be chosen. Ten
interferograms with different normal baseline lengths can be
simultaneously processed by this code at most. For the detailed
information about the input, output and parameters of this code, please
refer to the config.m and readme files in the code.

**2017-11-06**

[DOI: 10.21982/M8661Q] DMRT_QMS

Tsang, Leung; Tan, Shurun; Zhu, Jiyue

DMRT-QMS (QCA Mie scattering of Sticky spheres) v0.1
The code supports both active and passive remote sensing of layered snowpack.
It is an implementation of the dense media radiative transfer theory, applying
the scattering model of QCA Mie of densely packed Sticky spheres.
The radiative transfer equation is solved using the discrete ordinate method by
eigen-quadrature analysis.
Ground roughness is partially taken into account for the emissivity in passive remote
sensing and backscatter in active remote sensing.
In the snowpack description file, each row describes one snow layer,
starting from top, going downwards.
Each row contains five columns, specifying the
layer_thickness (cm), density (gm/cc), temperature (K), grain_diameter (cm), and stickiness,
respectively.

**2017-10-27**

[DOI: 10.21982/e0ms-rs71] LIBERTY (Leaf Incorporating Biochemistry Exhibiting Reflectance and Transmittance Yields)

Yang, Xiguang; Yu, Ying; Dawson, Terence P.

LIBERTY (Leaf Incorporating Biochemistry Exhibiting Reflectance and
Transmittance Yields) is a conifer leaf reflectance simulation model
based on radiative transfer theory. LIBERTY provides a simulation of
reflectance and transmittance of single leaf and quasi-infinite leaf
(stacked leaves) at 400-2500nm. The matlab version was compiled based on
the publication of Pro. T. P. Dawson on 1998. The inputs include leaf
structure and biochemical parameters. The outputs of the model include
reflectance of single leaf and quasi-infinite leaf and transmittance. A
user manual is provided, which contains the detailed description of
input/output parameters. A GUI interface make this program easy to
operate.

**2017-10-27**

[DOI: 10.21982/M8M92V] ISAR rapidly Spinning Targets 3D imaging

Mengdao, Xing

a novel 3-D imaging algorithm for rapidly spinning targets based on
target motion features. In this algorithm, a series of 2-D image slices
are generated based on the output of the matched filter bank. Then, the
image slices are combined to form a 3-D target image.
To get the final result, first you should run the function Data_Produce
to generate the simulation data. Then load the simulation data to make
match filter for three z coordinate respecticely. Finally,load the match
filter result and plot the 3D image.

**2017-10-27**

[DOI: 10.21982/M8S042] MTRC compensation

Mengdao, Xing

Effective methods for coherent processing and Migration Through Range
Cell(MTRC) compensation after translational motion compensation in ISAR
imaging. Available signal processing methods are Keystone Transformation
and Dechirp Clean.
Before you run the main function, run the function Data_Produce to
ensure that the simulation data has been produced.

**2017-09-18**

[DOI: 10.21982/M8S62C] Asymptotic methods for microwave scattering

Nouguier, Frederic; Chapron, Bertrand; Mouche, Alexis

Asymptotic Methods for backscattered Normalized Radar Cross Section
(NRCS) and geophysical Doppler shifts (GDS) from random linear sea
surfaces in the microwave regime.
Available asymptotics methods are:

* KA : Kirchhoff Approximation

* SSA : Small Slope Approximation

* GO2 : Geometrical Optics

* WCA : Weighted Curvature Approximation

Input parameters:

* Electromagnetic frequency/wavelength

* Permittivity

* incidence and azimuth for ongoing EM wave

* incidence and azimuth for outgoing EM wave (in bistatic case only)

* Ocean spectrum

* wind speed

* wind direction

Output parameters:

* NRCS

* GDS

**2017-06-26**

[DOI: 10.21982/M82K7J] Single Target Calibration Technique Code

Nashashibi, Adib

This code calibrates the measured backscatter response of a point target
using the Single Target Calibration Technique (STCT). The elements of
the scattering matrix of the target must be measured coherently. The
code loads all necessary measured data from files and manipulates the
input data before performing calibration steps. The code needs measured
data for the calibration target (metallic sphere) and the measured data
for the unknown target (target under test) that is intended for
calibration. All in ascii format.
It requires two measured data files for the cal_target (sphere). One of
the files contains the measured sphere data and the 2nd file contains
the measured background data (without sphere).
It also requires two data files for the unknown target (or target
under test) intended for calibration. One file is for measured
target data and the 2nd file holds background data.
All files hold the measured complex scattering matrix. Background data
may be ignored, however the user must modify the code to permit this
step.
Additional information that must be inputted by the user are sphere
size, range to sphere, range to unknown target, start and stop
frequencies, and number of frequency points used.
Samples of input and output data are included.
main code: stct_calibr_maincode.m
second. code: RCSmetallic_sphere.m
Calibr. target data: cal_target_data.dat (8 inch sphere)
Unknown target data: target_12inchSphere_data.dat
Sample output plot: CalibratedResponse_12inchSphere.eps

**2017-05-15**

[DOI: 10.21982/M81013] Line-by-line microwave radiative transfer (non-scattering)

Rosenkranz, Philip

Two main programs: one computes a downward-propagating
brightness-temperature spectrum at the bottom of the atmosphere; the
other computes an upward-propagating brightness-temperature spectrum
over a smooth ocean surface. These programs can be run as is, or read as
examples for using the subroutines in another application. The
programs ask for the frequency range, angle of propagation (from
vertical), and the maximum altitude at which to terminate the
calculation. If the altitude is >40km, the azimuthal angle of
propagation and the terrestrial magnetic field vector are also required.

**2017-05-10**

[DOI: 10.21982/M8JS3F] MCC

Emery, William

The Maximum Cross-correlation (MCC) method cross-correlates a template
sub-window in an initial image with all possible sub-windows of the same
size that fall within a larger search window of a second image. The
location of the sub-window in the second image that produces the highest
cross-correlation with the sub-window in the first image indicates the
displacement of that feature. The velocity vector is then calculated by
dividing the displacement vector by the time separation between the two
images.

**2017-04-06**

[DOI: 10.21982/M8W888] Multiple Layers Single Reflections

Cardellach, Estel; Fabra, Fran

Multiple Layers Single Reflections (MLSR) is a model for L-band
circularly polarized signals (such as GNSS signals) scattered off
layered media. It assumes that the reflection off each layer is
coherent, and that the signal splits into multiple path trajectories,
each path suffering one single reflection solely. The model first
computes the delay and amplitude of each reflected multi-path, taking
into account the refraction and reflection angles, reflectivities and
transmittivities at each interface, and attenuation along each layer.
Then it sums coherently all these contributions with their corresponding
amplitudes, shifting in delay and phase-delay.
INPUT: layers' permittivities or parameterization (density, temperature,
salinity...).

**2017-03-14**

[DOI: 10.21982/M8QG61] GNSS-matlab

Pascual, Daniel

Matlab functions to generate GNSS codes, signals and analytical spectra.
Includes example scripts, real data captures, official ICDs, and a
summary on GNSS signals.

**2017-01-26**

[DOI: 10.21982/M8301Q] RinexSNR

Larson, Kristine

Converts the standard GPS data format (RINEX) into useable data, i.e. it
computes the GPS orbits and calculates satellite azimuth and elevation
angle, and Signal to Noise Ratio data from GPS sensors. It does not
create soil moisture or snow depth by itself, but it will save a non-GPS
expert a lot of time.

**2017-01-19**

[DOI: 10.21982/M84S3Q] RSS Ocean Surface Emissivity Model

Meissner, Thomas; Wentz, Frank

1. Meissner Wentz model for the dielectric constant (permittivity) of
pure and sea water.
2. Ocean surface brightness temperature for 4 Stokes parameters as
function of frequency (6 – 90 GHz), earth incidence angle, sea surface
temperature, wind speed and direction.

**2017-01-12**

[DOI: 10.21982/M86P4P] GARCA/GEROS-SIM M2 (Instrument to L1 module) Web Online Simulation Tool

Park, Hyuk; Camps, Adriano; Pascual, Daniel; Kang, Yujin; Onrubia, Raul; Onrubia, Raul

GEROS-SIM M2 Web is the simple implementation of M2 (Instrument to L1
module) of GEROS-SIM. It is a web-based software to compute
Delay-Doppler Maps of GNSS Reflectometry in arbitrary configurations
(friendly to the GEROS-ISS configuration.) The simulator has inputs via
GUI: Receiver satellite height, sea surface height, elevation angle at
specular point, sea surface wind speed / direction, total electron
contents, and beam pointing errors. After the simulation, it produces
outputs: DDM, central Doppler frequency, and the other auxiliary data. A
user manual is provided, which contains the detailed description of
input/output parameters, and how to execute the simulation.

**2016-11-02**

[DOI: 10.21982/M8BC7Z] I2EM Backscattering from Single-Scale Random Surface

Fung, Adrian

This module computes the backscattering coefficient, σ^{0}, for a given random rough surface, using the I^{2}EM
model. Various parameters of the rough surface can be specified, such
as the dielectric constant ϵ = ϵ' -j ϵ'', the type of correlation
function, and the parameters of the correlation function. The model is
constrained to realistic surfaces with (rms height / correlation length)
≤ 0.25. ks is also constrained to be less than 1.

**2016-11-02**

[DOI: 10.21982/M8G59W] Polarization Synthesis of PolSAR Images

van Zyl, Jakob

Given a polarimetric image, this module synthesizes the radar image for
any specified transmit and receive polarization combination. Angles are
specified by the user for both the Rotation angle (ψ) and the
Ellipticity angle (χ) for both the transmit and recieve antennas.
The Ellipticity angle ranges from -45^{o} (right circular polarization) to 0^{o} (linear polarization) to +45^{o} (left circular polarization), while the Rotation angle ranges from -90^{o} (horizontal polarization), to 0^{o} (vertical polarization) to +90^{o} (horizontal polarization).
The code currently works with one image only.

**2016-10-27**

[DOI: 10.21982/M8KW2D] MIMICS version1.5a

Ulaby, Fawwaz; Sarabandi, Kamal; McDonald, Kyle; Whitt, Michael; Dobson, M. Craig; Dobson, M. Craig

MIMICS is meant to simulate the radar backscatter from a forested region
at frequencies in the P, L, and C bands. There are many parameters that
describe the soil, the trunks, the branches and the foliage. The code
using vector radiative transfer with PDFs of the canopy constituents to
produce estimates of the co- and cross-polarized backscattered powers.

**2016-10-25**

[DOI: 10.21982/M8QP4B] Reflection by Two-Layer Composite

Ulaby, Fawwaz; Pierce, Leland; Nashashibi, Adib

This module computes the reflection properties of a two-layer composite with planar boundaries. Medium 1 is air with ϵ_{1}
=1. The incidence angle in medium 1, and the frequency in GHz also are
inputs. The reflection coefficient and reflectivity are plotted against
the thickness of the top layer, for both h and v polarizations.
inputs: complex dielectric constants for 2 layers, incidence angle,
frequency
outputs: plots: Reflection Coefficient Magnitude vs. layer thickness,
Reflectivity vs. layer thickness

**2016-10-25**

[DOI: 10.21982/M8159V] Propagation Constant and Intrinsic Impedance

Pierce, Leland; Nashashibi, Adib; Ulaby, Fawwaz

Code computes attenuation and phase coefficients and intrinsic impedance
of a lossy or lossless medium over a specified frequency range.
inputs: complex dielectric constant
outputs: plots: Attenuation coefficient vs freq, Phase coefficient vs.
freq, Magnitude of intrinsic impedance vs. freq, Phase angle of
intrinsic impedance vs. freq