DSP Question Nyquist Sample Rate

[steppermotor]

Question: A continuous-time signal x(t) = cos(f(t)), where f(t) = w0 + sin(w0t), is to be sampled at a rate fs.

What is the system’s Nyquist sample rate if w0 = 1000/(2pi) r/s?


I believe that w0=2*pi*f --> f= (1000/2*pi)*(1/2*pi) = 25.33 Hz and then multiplying by 2 to get the Nyquist sampling rate of: 50.66 Hz.

Am I on the right track or do I need to take into account the w0+sin(w0t) in some manner. I thought about taking the derivative: w0cos(w0t), but not sure how this helps me.

 

[flashking]

Nyquist rate must be double the highest frequency

since f(t)= w0 + sin(w0t) then MAX[f(t)]= w0 + 1

because the maximum value for sin function is 1

so Fs = (w0 + 1)/pi

I guess

 

[:pH]

Nyquist rate must be double the highest frequency

since f(t)= w0 + sin(w0t) then MAX[f(t)]= w0 + 1

because the maximum value for sin function is 1

so Fs = (w0 + 1)/pi

I guess

This is completely wrong logic about the nyquist criteria , it simply says "For proper reproducibility of a signal , the sampling rate must be ATLEAST twice the maximum frquency component in the signal" , now w0 term just presents a VARIABLE DC offset at every frequency instant of sampling in time domain , so we do not have to consider it for sampling frq analysis.

I believe that w0=2*pi*f --> f= (1000/2*pi)*(1/2*pi) = 25.33 Hz and then multiplying by 2 to get the Nyquist sampling rate of: 50.66 Hz

Yep , exactly , thats the minimum frequency of sampling required

---------- Post added at 07:36 ---------- Previous post was at 07:36 ----------

hope it helped !!!

 

[permute]

it depends on how many side lobes you want to retain.

quick ref with pic: http://crca.ucsd.edu/~msp/techniques/v0.08/book-html/node83.html

 

[ninju]

If you take a sin(2*pi*fc*t) and sample it at fs=2fc, then you get sin(2*pi*fc*n/fs). fs=2fc. So, sin(2*pi*fc*n/(2*fc)).

On simplifying, you get, sin(n*pi) which is 0 for all n. So, even though you satisfy the nyquist rate, you'll be sampling at all points that have a zero value. In case of cosine signal, you'll get all ones. So, use a value greater than twice the nyquist rate. Regarding the nyquist rate for your question, i'd go with what flashking told.

@ph: the question says sample x(t)= cos( w0 + sin(wo t)).

 

[:pH]

@ph: the question says sample x(t)= cos( w0 + sin(wo t))

oops , my mistake , flashking , thats true