Digital Signal Processing Reference
In-Depth Information
(b)
h
=
(
−
0
.
1
n
)
0.9
n
u
[
n
]
0
.
1
n
))0.9
n
u
(c)
h
=(1+(
]
(d)
h
=
0.5*exp(j*pi/2).ˆ(0:8) + 0.5*exp(-j*pi/2).ˆ(0:8)
17. Write the m-code for the script
−
[
n
LV xMatchedF ilter(NoiseAmp, T stSeqLen, F lipI mpResp)
that generates a test signal of length
T stSeqLen
consisting of a chirp of a given length (less than
T stSeqLen
) immersed in noise having amplitude
NoiseAmp
and length
T stSeqLen
which can be
convolved with either the chirp of given length itself or a time-reversed version of it, according to the
input argument
FlipImpResp
, which can assume the value 0 to use the non-time-reversed chirp as a filter
impulse response or 1 to use the time-reversed chirp as the filter impulse response. Plot the impulse
response being used and the test signal, poised to begin convolution, on a single plot, and the convolution
sequence on a second plot. The function specification is as follows:
function LVxMatchedFilter(NoiseAmp,TstSeqLen,FlipImpResp)
% Forms a test impulse response, a chirp having a length equal
%
to half of TstSeqLen, then builds a test sequence having
%
length TstSeqLen and containing the chirp and noise of
%
amplitude NoiseAmp. The test signal is then convolved with
%
either the chirp or a time-reversed version of the chirp, and
%
the results plotted to demonstrate the principle of matched
% filtering.
%
FlipImpResp: Use 1 for Time-reversed, 0 for not time-reversed
%
impulse response.
% Test calls:
% LVxMatchedFilter(0.5,128,0) % imp resp not time reversed
% LVxMatchedFilter(0.5,128,1) % imp resp time reversed
18. Write the m-code for the script
LVxTestReconSineVariablePhase(k
1
,N,PhaseDeg)
receives a frequency
k
1 and length
N
to be used to construct three sinusoids, which are 1) a sine wave
of arbitrary phase
PhaseDeg
and frequency
k
1, and 2) a test correlator sine of frequency
k
1 and 3) a
test correlator cosine of frequency
k
1. Compute the correlation coefficients using Eqs. (4.7) and (4.8),
and then reconstruct the sine wave of arbitrary phase
PhaseDeg
and frequency
k
1 using Eqs. (4.9)
and (4.10). Plot the test sine wave, the two correlators, and the reconstructed test sine wave. The function
specification is as follows:
function LVxTestReconSineVariablePhase(k1,N,PhaseDegrees)
% Performs correlations at the zeroth lag between
% test cosine and sine waves of frequency k1, having N samples,
%
and a sinusoid having a phase of PhaseDegrees, and then
%
reconstructs the original sinusoid of phase equal to
%
PhaseDegrees by using the CZL values and the test sine
%
and cosine.
%Test calls:
% LVxTestReconSineVariablePhase(1,32,45)
