The Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.
2
votes
1answer
62 views
How to derive stability of analogue and digital systems
I'm trying to find out why digital systems are stable iff poles oh their transfer function are inside the unit circle (or are there any others conditions?).
I understand analogous systems are stable ...
3
votes
1answer
61 views
Why is a feedback loop not represented by the least order transfer function?
I have a feedback loop with transfer $L(z)= \frac{H(z)C(z)}{1+H(Z)C(z)}$.
$H(z) = h$ and $C(z) = \frac{K}{z-\alpha}$.
If I manually calculate the transfer function, I get:
$L(z) = ...
4
votes
2answers
84 views
Can I determine a system's $z$-domain transfer function from its pole-zero plot?
Is it possible to generate the z-domain transfer function from a pole-zero plot diagram?
3
votes
1answer
55 views
Is this a valid z-transform of $ \frac{1}{n^2}u[n] $?
I was looking over some DSP and came across the following signal: $x[n] = 1/n$. So I wondered whether it had a z-transform but I soon realized that it fails to meet two conditions described here:
...
5
votes
2answers
126 views
Find the frequency response of a system
I'm trying to find the frequency response $$H(\omega) = Y(\omega)/X(\omega)$$
for this system- the signal equations are given:
$$y[n] = v[n - M] - g * v[n]$$
$$v[n] = x[n] + g * v[n - M]$$
I've tried ...
5
votes
1answer
169 views
Z-transform of a downsampler
In this paper or multirate filtering, the author establishes the following mathematical relationship. Let $y_D$ be the output of a downsampler such that
$$y_D[n] = x[Mn]$$
where $M$ is the ...
7
votes
1answer
146 views
Filter order estimation
Assume some unknown but small and finite number of poles and zeros in the complex Z plane, all with complex conjugates, producing some response. Strictly from the absolute value of a set of equally ...
1
vote
2answers
240 views
Understanding the transfer function of an FIR filter
I'm currently studying FIR filter and am having trouble understand how the following equation works, and it's implication.
$$ y[n] = h[n] * z^n = H(z) \cdot z^n $$
I don't really understand how this ...
7
votes
2answers
191 views
What is the Z-transform of Bessel function $J_0(\alpha n)$ sequence
What is the Z-transform of the sequence $J_0(\alpha n)$ for $n \in \mathbb{Z}$?
The Fourier transform of zeroth order Bessel function $J_0(\alpha x)$ is known to be $\frac{2}{\sqrt{\alpha^2 - ...
8
votes
1answer
179 views
Finding the z-transform of $h[n] = a^n\cos(2\pi \frac{n}{F_s}f_0)$ for $n ≥ 0$ and zero for $n < 0$
So I'm trying to decide whether the cosine part is intended to be plugged in for $z$ or whether it is strictly part of $h[n]$. (the number a lies in the open unit disk)
I mean I was pretty sure it ...
7
votes
1answer
2k views
How does the Z transform's “region of convergence” work?
I'm a novice in DSP and I have few doubts regarding the Z transform and its region of convergence (ROC).
I know what a Z transform is. But I'm having trouble with understanding the ROC. First of all ...
