# Tagged Questions

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### Fourier and $Z$ transform of a signal?

We have $$X(k)=4[u(k-2)-u(k)* d(k-3)]$$ I need to find the Fourier transform,$Z$ transform,as well as dhe magnitude and phase spectra. First of all I think that I need to convert the $u(k)$ and ...
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### If $tf(t)=tg(t)$, where $f(t), g(t)$ are distributions, then $f(t)=g(t)+λδ(t)$.

Using Dirac distribution properties, prove that if $tf(t)=tg(t)$, where $f(t), g(t)$ are distributions, then $f(t)=g(t)+λδ(t)$. If someone knows please help me how to start the proof. Thank you
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### Help with transfer function H(s)

i have the transfer function $H(s)$ as in the picture http://imagizer.imageshack.us/a/img836/9336/ecc2.jpg In the first question I need help to find $\vert H(s) \vert$ for a constant signal. What do ...
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### Sketching the spectrum of a signal

The figure below shows Fourier spectrum of a signal $g(t)$ Sketch the spectrum of the signal $2g(t)\cos^2(100\pi t)$. Show value in sketch.
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### Finding the period of complex exponential function

I am having some trouble finding the period of the following discrete signal: $x[n]=e^{jn2\pi/3}+e^{jn3\pi/4}$
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### when is phase information protected?

I have general question that when is the phase of a signal protected in time domain and frequency domain and vice versa? can anybody help me? Thanks in advance.
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### Frequency response of Continous-time system

Not sure where to start on this one: $$H(s)={(s-j\omega_0)(s+j\omega_0)\over(s+\omega_0\cos\theta+j\omega_0\sin\theta)\left(s+\omega_0\cos\theta-j\omega_0\sin\theta\right)}$$ Sketch the frequency ...
121 views

### Z-Transform, Transfer Function, Poles & Zeros

I've been working on a question that I'm now stuck on. I need to: Determine the transfer function and poles-zeros of: $y[n]=0.5y[n-1]-0.25y[n-2]+x[n]$ So far I've carried out a z-transform in ...
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### Convolution of indicator function with itself

A paragraph in Mallat's "A wavelet tour of signal processing" says: Spline Dyadic Wavelets A box spline of degree $m$ is a translation of $m+1$ convolutions of $\mathbf{1}_{[0,1]}$ with itself. ...
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### Harmonic mean of absolute value squared discrete Fourier transform

Let $X[k] \in \mathbb{C}$ be the discrete Fourier transform of $x[n] \in \mathbb{R}$, where $k,n = 0,1,2,...,N-1$. Parseval's theorem relates the arithmetic mean (AM) of absolute value squared ...
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### When writing out the wave equation isn't the phase shift just adding to the frequency?

I hope someone here could clarify for me. With the waveform function f()=(A)sin(wt + theta) where A=magnitude of the wave, sin= type of wave form, wt=frequency rads/sec, theta = phase shift ...
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### Region of convergence of Z-Transform connected area?

Shouldn't the Region of Convergence of the Z transform be a connected area ? In Oppenheim solution manual, I've found this answer of a question that asks to determine the different forms of the ...
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### How to illustrate the transfer function with a given equation?

Homework/Revision question: Define the transfer function of a linear system. Illustrate your answer by considering the system governed by the equation: $\frac{dy}{dt}+ay=bx$ where x and y are ...
323 views

### How to extract module and phase from this transfer function?

I have this transfer function: $$H(x)= \frac{1}{x+i(1+x)}$$ How can I extract module and phase and represent them?
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### How to Find Phase Lead/Lag

I have the transfer function $$H(s) = \frac{s+1}{0.1s+1}$$ I apply the Bilinear Rule with a sampling time T =.25 sec to the transfer function and get a z-domain representation of H(z) = ...
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### Period of a product of $\sin$ and $\cos$

I want to find the period of $\sin(t) \cos(\pi t)$. I started off by transforming that into $\frac{1}{2}\left [ \sin((\pi +1)t) - \sin((\pi - 1)t\right ]$, but then I get stuck. How do I find the ...
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### Haar Basis in Signal processing

I want to help one of my friends who studies engineering. He has a homework at the signal processing course. I think I realize what I have to do, but since I don't have their course, I do not fully ...
I'm having a terrible time trying to understand Fourier transforms. I'm very visual so leaving the $X,Y,Z,t$ domain is not working form me :) I'm trying to figure out the basics at the moment. ...