# Tagged Questions

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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### Discrepancy when calculating LTI system output using inverse z-Transform

I'm given a difference equation, $y[n]-0.4y[n-1]=x[n]$, and asked to find the natural response $y_n[n]$, forced response $y_f[n]$ and complete response $y[n]$ if $x[n]=4 (0.25)^nu[n]$ and $y[0]=0$. ...
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### transform function with non-linearity

I'm a newbie to Signal Processing - my apologies if this question is too obvious (I'm a financial trader trying to use DSP techniques). For a linear filter: $y[n] = (1-p) x[n]+p y[n-1]$ we can the ...
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### Evaluating the inverse Z transform on the unit circle

I am trying to understand the math. The inverse z-transform is given by: $x[n] = \displaystyle\frac{1}{j2\pi} \int_cX(z)z^{n-1}dz$ where $\int_c$ is a contour integral. The inverse Fourier ...
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### Determining which Filter from a Z-Plane Plots?

How do i determine which FIR filter (LP, HP, BS, BP) it is from looking at it's z-plane plot?
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### For linear IIR digital filter, what happens for negative frequencies?

By negative frequency, I refer to Fourier transform. Often, the frequency response of a digital filter is only displayed for positive frequencies. For a linear IIR digital filter, what happens for ...
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### Z-plane/S-plane to time domain?

I'm working through the IIR chapter in Dick Lyons' Understanding DSP, and there's something I'm having a hard time wrapping my head around. He'll draw poles and zeros and then show the associated time ...
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### Why Z-transform is considered as separate transform?

The mathematical formula of the Laplace and Z transforms are same with just one difference. I.e. in the first we use $t$ for continuous-time signal and in the latter uses $n$ for discrete-time ...
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### What is the mathematical interpretation of using direct inversion around a single pole/zero

Let $F[z]=N^2\frac{z(z-(3+j\sqrt{7})/2)(z-(3-j\sqrt{7})/2)}{(z-1)^3}$ This has 3 poles at $z=1$; one zero at $z=0$; and a conjugate pair of zeros at $z=\frac{3\pm{}j\sqrt{7}}{2}$ Assuming a contour ...
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### Finding minimum phase version of 2D impulse response?

For a impulse response $\mathbf{h}=[h_0 \space h_1 \space … \space h_n]$, one can find a always find a minimum phase version of $\mathbf{h}$ by using an appropriate All-Pass system. For my problem, ...
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### Can the Z-Transform be used to create smoothed 3D surfaces from point clouds?

According to Dr. Math the Z-transform can create closed-form solutions for 1D series defined by difference equations (e.g. the Fibonacci series). My 3D surface $z=LC(x,y)$ is defined by difference ...
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### When sinusoidal input starts at n=0, why are transient response associated with z-transform poles of digital filter?

In http://www.eng.ucy.ac.cy/cpitris/courses/ECE623/presentations/DSP-LECT-10-11-12.pdf, it says that when sinusoidal input $X(z)$ starts at n=0 (with n<0 having zero input) and the input passes ...
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### what is the name of this curve

I was drawing a high pass filter response ,in a polar coordinates, the function is (z+1)/z and then it is 2+2*cos(w) the plot is ...
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### Given the digital filter, how does one minimize transient reponse while keeping steady-state resposne?

Suppose the digital filter is given by $H(z)$. If the input is $0$ for $n<0$, then when input occurs at $n =0$, transient response will necessarily be there. So I want to minimize this transient ...
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### Can poles of z-transform transfer function be zero to eliminate transient response?

I believe that answer to "Can poles of z-transform transfer function be zero to eliminate transient response?" is no, but I am not sure why it's no.
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### transient response of simple digitalized RC low-pass filter

In http://en.wikipedia.org/wiki/Bilinear_transform#Example, digital version of simple RC low-pass filter is presented: $$\frac{1 + z^{-1}}{(1 + 2RC / T) + (1 - 2RC / T) z^{-1}}$$ where $T$ is ...
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### Checking convolution property II of z transform

I have two sequences x and y of lengths, say 5 and 10. I multiply them in time domain element by element. I get another sequence. Now this as per the convolution theorem should be equal to the ...
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### Inverse z transform - contour integration

Here is my task: Find inverse z transform of $X(z)=\frac{1}{2-3z}$, if $|z|>\frac{2}{3}$ I need to find it using definition formula, $x(n)=\frac{1}{2\pi j}\oint_{C}^{ } X(z)z^{n-1}dz$. How can I ...
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### What is the significance of Z-transform?

As we have in Laplace transform that the roots decide the stability of the system i.e. if the roots are complex and lie in the left side of the plane you get a sinusoidal response with decreasing ...
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### Visualising a Z-transformed Transfer Function?

For designing any analog filter and various other outputs of filter we use laplace transform,I can visualise a laplace transform like for ex. s[X(s)] can be ...
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### Difference Equation & Impulse Response of IIR filter - deconvolution

What i want to do is to design an IIR-filter that cancels the "echo", such that im only left with the delta[n]. To do so i ofcourse make an IIR-filter, where u take the z-trans of the impulse ...
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### Pole/Zero existence at infinity

How can poles and zeros exist at infinity?Can anybody explain using a system function?
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### Study Signal Processing

I'd Like to ask two questions : What is the difference between studying Signal processing (both Deterministic and statistical) in Department of Electrical Engineering versus Department of Mathematics ...
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### Real and Imaginary Frequency Responses of a single complex pole

I'm filtering a real signal with a single complex pole with a complex coefficient (a_re [real part] and a_im [imaginary part]), I also have a gain coefficient but I'm gonna leave it out for the sake ...