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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Please explain Multiplication property in Z transform?
I am having problem visualizing contour any example will be great help.
As far as as where I need it I was trying to find Z transform of a contracted signal by first multiplication by impulse train.
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Determine filter type using recurrence relation
Given the recurrence relation:
$y[n] = x[n] + 0.5y[n-1]$
I want to determine the filter type (i.e. LPF, HPF etc.)
I try to use Z transform, and get that the the transfer function is
$H(z) = \frac{2z}{...
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DTFT of $ f[k] = 3^k u(-k-1)$
Find the Discrete-time Fourier transform of $ f[k] = 3^k u(-k-1)$
(then sketch it and find its magnitude & angle).
It doesn't fit any templates on the Fourier table, and I don't see how one ...
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z-transform of $2^k$
It seems that you can decompose it as such:
$f(n) = a^n u(n) + a^{-n} u(-n-1)$
But I already have issue here,
is it basically saying that $ u(n) + u(-n-1) = 1$?
this is the plot of u(n) and u(-...
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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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IIR filter SOS and Direct Forms doubt
I have below doubts, so confusing! As I don't want to assume from what I read, I am asking for help here!
Are Second Order Sections another name for biQuads ?
If I have 2 single pole transfer ...
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Why the number of poles and zeros for a RHS signal in the Z domain is equal?
I can not understand the reason why the following sentence is true:
If we have a Right-Hand signal(RHS) x(n), X(z), the Z-transform of x(n), has the same number of poles and zeros except at z = ...
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How to compute the inverse Z-transform
How to compute the inverse Z-transform of the form $$ G(z)=\frac{z^{2n}}{a(z^{2n})+b(z^n)+c} $$
I started by taking
$$ F(z^n)=G(z) $$
so
$$ \frac{F(z)}{z}=\frac{z}{az^2+bz+c}$$
This can be solved ...
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Digtial FIR Impulse response & transfer function
I am currently working the figure through below.
as it is an FIR Filter i have worked out using convolution that the output is 4,2,4,6,0,0.
i am trying to obtain the 'z' domain transfer function of ...
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Calculating the output of a pole eigen signal in a difference equation
Let an IAR system be defined by the following difference equation:
$$y[n]-\frac{1}{4} y[n-2]=x[n]+3x[n-1]$$
and an input signal $x[n]=(-0.5)^n$.
The transfer function is defined as $H^z(z)=\frac{1+3z^{...
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How do I find the ROC of a system if it has no poles
The output of a system of discrete time $y[n]$ is corellated with the input $x[n]$ through the equation $y[n]$.
$$y[n] = \frac 13\big(x[n-1]+x[n]+x[n+1]\big)$$
It then asks me to find the system ...
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Taking the inverse $\mathcal Z$- transform with a summation in the denominator
I'm learning about z-transforms, and was going through some practice problems and I've been stuck on this one for a little bit. I'm trying to take the inverse z-transform of the following:
$$\frac{1}{\...
