# Questions tagged [z-transform]

The Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.

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### Inverse Chirp Z Transform

I am working to understand and use the Chirp Z-Transform. I want to use the algorithm for simple signal processing on data sets that are not a power of two. I need to be able to inverse transform as ...
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### Z-transform and binomial series

I am reading a paper on frequency warping and I need to do a little manipulation of the Z-transform. Can somebody help me on how can I go about deriving equations $(3)$ and $(4)$ from equations $(1)$ ...
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### Does the ROC (Z-Transform) always start/end from/in a pole?

Can I assume that the R.O.C. from a Z-Transform will always start from or end in a pole or 0/infinity? Using an example: $$H(z)=\frac{(z+1)(z-1)(z+j)(z-j)}{z^4}\space,\space\space j=\sqrt{(-1)}$$ ...
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### Transformed Direct Form II filter: Z transform: reduce multiplications

In the diagram below there are three multiplication operations required to compute each filter output sample. I'd like to draw a block diagram of an equivalent filter but requiring fewer than three ...
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### 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?
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### 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: .....
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### 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 ...
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### 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 ...
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### 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 ...
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 ...