Hi milesyoung.
That's FT pair from my book. Is it wrong?
I found time shifting property in my book: if function is $$f(t\pm t_0)$$, FT is $$e^{\pm jw_0t_0}F(jw)$$. So FT of time shifted term would be $$e^{\pm jw(\frac{\pi}{2}+\theta)} F(jw) $$, right?
[FONT=Georgia]This my homework:
Input signal to system is:
where
H(exp(jw)) is transfer function of ideal low pass filter with cutoff frequency wg=3*pi/4 and zero phase characteristic. Sampling in A/D converter is done with period T=(1/125) seconds.
a) Calculate output signal ya(t)
b)...
Here is how I tried to solve this algebraically.
We have function u(n+N)-u(n-(N+1)). Let's say N is some positive number, for example N=1.
1. When n is less then -N, for example n=-2, we have u(n+N)-u(n-(N+1))=0-0=0.
2. When -N<n<N+1 , for example n=-0.5, we have u(n+N)-u(n-(N+1))=1-0=1.
3. When...
Thanks for reply.
One more thing. Let's say I have some circuit with nonperiodic voltage source and I want to find response of some component in circuit, for example voltage across component. Using Fourier transform I should "convert" my excitation from time domain to frequency domain, find...
Hi. Here is one example from my book.
Calculate Fourier transform of signal:
Here is solution:
We can write x(n) as:
,
where x1(n) is u(n+N)-u(n-N-1). We can write:
(we used that cos(n)=(1/2)*(exp(j*n)+exp(-j*n)).
Using properties of Fourier transform of discrete signal:
,
Fourier...
Hi. I'm familiar with Fourier series but I have some hard times in learning Fourier transform. Why we use it? What's purpose of Fourier transform? Here is one signal and plot of Fourier transform of that signal:
What this graph tells us? Thanks in advance.