Matlab newbie, I need help with fft of sin/cos functions

[Dexter2011]

Hi all!

I am a complete Matlab newbie. I have an assignment to complete in Matlab, and I am having some, what I am sure, are elementary difficulties. My assignment is using the Fourier Transform function. Here are the instructions:

1. Generate the following functions:
y1(t)=2*sin(2*pi*1*t)+4*sin(2*pi*2*t)+3*sin(2*pi*4*t)
y2(t)=2*cos(2*pi*1*t)+4*cos(2*pi*2*t)+3*cos(2*pi*4*t)

2. First, required by sampling theorem, the step size of t (delta t) has to be smaller than a value. Figure out this value and set delta t at least 3 times smaller than this value and calculate y1(t) and y2(t).

3. Calculate Fourier Transform (fft) of y1 and y2 and plot your results using frequency as the x axis and amplitude as the y axis. Plot the phase also.
Given:
f=[0:1/length(y1):1/2]*(1/delta t)
plot(f,abs(y1(1:length(f)))'-*')

...Ok, as for #1 and 2, I think I know how to get the delta t. I am not sure how to define time. I have searched the web and found several similar but differing functions: t=(0:n-1)*(1/fs); t=(0:1/fs:n); etc. Where do I get the n? Which equation do I use?

And for #3, I am not sure how to define frequency. Again, I have found several functions differing slightly. For example in the given frequency equation, what is the length(y1)? Why is frequency defined from 0 to 1/2...where does the 1/2 come from? And where do I get the length(f)?

I'm sure these are basic questions, but I am in a grad class where I believe we are expected to already know Matlab and this is literally my first go at it. I would really appreciate any help you could give.

Thank you!!

 

[MHanif]

Hi Dexter
I think you should have been taught a course on Digital Signal Processing in which you are told how to sample a continuous time signal. As you know that if x(t) is a continuous time signal and x[n] is its discrete time representation then x[n]=x(nT) where 'T' is the sampling time which you have written 'delta t'. So, time t is t=nT where 'n' is the discrete time index say having values 0,1,2,...,N-1. So, t=(0:N-1)*T where T=1/fs.

Now you also know the relationship between the frequencies of Fourier transform of x(t) and x[n]. In fact if F is the frequency of continuous time signal and f is that of discrete time then
f=FT
for -0.5<=f<0.5
So,
F=(0:length(y1)-1)/(length(y1)*2)*1/(delta t).
where length() is MATLAB's function returning the length of a variable like if A=[1 -1 6 5]; then length(A) will be 4.

 

[Dexter2011]

Hi MHanif,

Though I am in a graduate engineering program, my undergrad is in Math, and I have never taken an engineering course before. So unfortunately, this is all very new to me, and I've had to just dive in head first. Your explanation helped me a lot, and I understand this aspect of Matlab now. So thank you so much!!!

Dexter