0
votes
1answer
13 views

Expressing array response $A(Z) = \sum_{-N}^{N} w_n Z^n$ as sine-function

The array-response of an antenna can be defined as: $$A(Z) = \sum_{-N}^{N} w_n Z^n$$ where $Z = \exp(-i \omega \Delta t) = \exp(-ik\Delta x \sin \alpha)$ According to my textbook, if we let $w_n = ...
2
votes
2answers
69 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 ...
32
votes
10answers
1k views

What's the difference between $\mathbb{R}^2$ and the complex plane?

I haven't taken any complex analysis course yet, but now I have this question that relates to it. Let's have a look at a very simple example. Suppose $x,y$ and $z$ are the Cartesian coordinates and ...
0
votes
2answers
74 views

Complex expression for periodic binary sequences

We have infinite binary sequences of type $$\langle g_n \rangle_{j=4}=\{0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,...\} \,;\, n\to\infty$$ where $j$ indicates the length of a period that starts/ends with a $1$; ...
1
vote
1answer
139 views

How can I calculate the bode magnitude and frequency as well as their plots?

I've been trying to figure this problem out for a while now. I've been given a transfer function $$H(s) = \frac{s(s+100)}{(s+2)(s+20)}.$$ I'm supposed to calculate the bode magnitude and frequency for ...
1
vote
1answer
479 views

FFT with a real matrix - why storing just half the coefficients?

I know that when I perform a real to complex FFT half the frequency domain data is redundant due to symmetry. This is only the case in one axis of a 2D FFT though. I can think of a 2D FFT as two 1D ...
1
vote
1answer
194 views

Complex Numbers and polar form

I am given the following information: $$x[n]= s^n,\qquad n=0,\pm 1,\pm 2,\ldots$$ where $s=\sigma + j\omega = re^{i\theta}$ is a complex number in general. I was wondering how the following is ...
2
votes
3answers
453 views

Simplifying the expressions for the magnitude and phase of a Fourier transform

$$h[n] = 2( \delta[n-2]-\delta[n-1]-\delta[n-3])$$ i computed my frequency response and i have this now: $$H[e^{j \omega}] = 2[ e^{-2 j \omega} - e^{-j \omega}-e^{-3 j \omega}]$$ $$H[e^{j \omega}] = ...