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3 votes
Accepted

Create a minimum phase filter from an elliptic digital filter

The impulse response hmp is computed by convolving the impulse response of the elliptic filter with itself. We know that the elliptic filter is marginally minimum-...
Matt L.'s user avatar
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2 votes

Create a minimum phase filter from an elliptic digital filter

A filter is minimum phase when all it's poles and zeros are inside the unit circle. The easiest way to check is to inspect the zeros and poles of the filter and look at the magnitudes ...
Hilmar's user avatar
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1 vote
Accepted

Inverse of a causal and stable system

If a given system with a rational transfer function is causal and stable, we know that its poles must lie inside the unit circle. Consequently, the inverse system, whose zeros are the poles of the ...
Matt L.'s user avatar
  • 90.4k
1 vote
Accepted

Why is $y(n)=Ax(n)+B$ not relaxed if $B\neq 0$?

By definition, a linear system is said to be relaxed at time $t_0$ if and only if $y(t) = 0,\forall t\leq t_0$ (no stored energy in the system). With this definition, the affine dynamic system $y(t) = ...
AHT's user avatar
  • 379
0 votes

Why does twice the sampling rate (Nyquist Theorem) seem inadequate?

"a sine wave with only 2-3 samples per period looks very ugly even though it obeys this rule. It looks more like a triangle wave." This is an old question but I still think it's worth it to ...
cebola's user avatar
  • 1
0 votes

Is it possible to find the FFT of a 1024-point signal by taking 8-input points at a time and calculating the FFT of those 8-points until the end?

There is a divide and conquer approach to computing the FFT detailed in this PDF. Here is an implementation as in section 8.1 ...
rtclark's user avatar
  • 121
1 vote
Accepted

Amplitude scaling for the FFT of a logarithmic frequency sweep

Let's look at the the spectrum on a log/log scale to see what's going on You can see that the sweep starts indeed at 1Hz and goes all the way up to 5kHz. However the spectrum is not flat, but it's ...
Hilmar's user avatar
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3 votes
Accepted

finding the coefficients of the following difference equation so that it holds true

Here is one possible solution. Recognise that the finite difference equation is a convolution between the signal and a finite impulse response filter. The z transform of x[n] is: $$x[z]=\frac{Arz^{-1}\...
Stephen's user avatar
  • 391
4 votes
Accepted

Z-transform of the Unit Step and DTFT

Assuming that the $\mathcal{Z}$-transform $X(z)$ of a sequence $x[n]$ exists, there are three cases we need to distinguish when considering the relation between $X(z)$ and the corresponding DTFT $X_F(...
Matt L.'s user avatar
  • 90.4k
2 votes

Frequency components in graph signal processing

It seems that in many cases, the principal harmonics do not offer meaningful insights. Recent work on combinatorial Hodge theory has given us interesting ways to form insights on discrete Laplace ...
Georg Essl's user avatar
1 vote

What is the correct interpretation of the capacity formula with modulation?

since $(2) > (1)\quad\forall M>2$, and $(1)$ is an upper bound, $(2)$ must be incorrect, assuming it describes the same $C$.
Marcus Müller's user avatar

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