Tagged Questions

1answer
45 views

Why would the discrete fourier transform “see” signals like this? What is the origin of spectral leakage?

The discrete fourier transform of $x = (x_{0},\dots,x_{N-1})$ is defined as $\displaystyle X_{k} = \sum_{n=0}^{N-1} x_{n}\omega^{kn}_{N}$ where $\omega^{kn}_{N} = e^{-2\pi ik/N}$ and ...
1answer
41 views

Impulse response and z transform question?

We have $g(k)=\{ [(1/5)^k]u(k)\text{ for$1 \le k\le3$and$0$for other }k\}$ The input is $x(k)=\delta(k) +3\delta(k-1)+ \delta(k-2)$ Using Z transform we have to find the output $y(k)$ and the ...
1answer
69 views

How do digital filters work in time domain?

I am trying to understand how do digital filters work and how to actually calculate the output numerically. I have read that they are characterised by a transfer function $H(z)$ which results in a ...
2answers
269 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
1answer
92 views

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 ...
3answers
227 views

Pre–emphasis - Signal Processing

I am trying to compute the Pre-emphasis of a signal and the formular is below: y[n] = x[n] - 0.95 x[n-1] Let: ...
0answers
249 views

Understanding Discrete Cosine Transformation

I'm currently working on some software and a key component is 2D DCT. But my question is more general, as I'm trying to understand the DCT in general, let's say from engineers point of view. For ...
1answer
681 views

Finding Fourier series with function not centered at the origin

I am trying to find both Fourier cosine and sine series which represent the function F(t) in the interval $(0, \pi)$ where \$F(t)=\begin{cases} \frac{\pi}{2} & \ \ 0<t< \frac{\pi}{2}\\ 0 ...
2answers
137 views

Z-Transform Identity

I've come across an identity and would like to know if it has some sort of formal name or derivation or explanation or something! Also, I'm curious as to whether others are aware of such an identity. ...
0answers
300 views

Fast Walsh–Hadamard transform generalization for non-power-of-two orders?

I have to process vectors through a Hadamard matrix of order N. If N is a power of 2, I can use the Fast Walsh–Hadamard transform; but if N is not a power of two (for instance, N=12), it is not ...