# Decimation of signal. How to plot frequency spectrum

I have an FDM signal from 0 to 70 MHz. The total signal contains 4 FDM signals from (0-fs/4), (fs/4-fs/2), (fs/2-3fs/4) & (3fs/4-fs). I used fvtool command in matlab to plot these signals. Then i downsampled the total signal by 4. Downsampling is time is expansion in freq spectrum. Thus on paper my new signal should occupy freq (0-fs), (fs-2fs), (2fs-3fs) & (3fs-4fs) When i plot this downsampled signal using fvtool again, i am just able to see my 1st FDM signal ie b/w (0-fs/4) appearing in the plot. How to view the entire spectrum from (0-4fs) in fvtool.

The root of your problem is that you are not familiar with the Nyquist Sampling Theorem.

First of all, I question your premise that your sample rate is 70 MHz and that you can represent your signals, which range from 0 to 70 MHz, at this rate. The Nyquist sampling theorem indicates that you can only represent signals up to half the sample rate, which is 35 MHz in your case.

When you downsample by a factor of four you are reducing your sample rate by a factor of four, which in turn reduces the frequencies that you can represent by a factor of four. You are thus aliasing your signals, causing them to all be at the same frequency. Thus, the one signal that you see after you downsample is really all four signals packed into one slot.

• Sorry. My sampling frequency is not 70 MHz. I got confused. I have take nyquist rate into account in my problem. Jun 26 '13 at 3:25

The problem seems to be aliasing. According to this if i want to downsample my signal by M then it must be band limited to fs/M. So, if i want to build a polyphase DFT filter of order M, then to get each individual signal at each filterbank output, i must band limit my input FDM signal to fs/M. Is that correct or am i missing something

• You're on the right track now, but still not quite right. You need to limit your signal to $\frac{f_s}{2M}$. If your samples are complex it can be from $\frac{-f_s}{2M}$ to $\frac{f_s}{2M}$, giving a total possible bandwidth of $\frac{f_s}{M}$. Jun 26 '13 at 21:32
• But after generating the signals from -fs/2 to fs/2, i gave a shift of fs/2 so that my signal lies from 0 to fs. Jun 27 '13 at 3:10
• That will cause the signals from fs/2 to fs to alias. Jun 27 '13 at 13:34
• Sorry, i again made a mistake in previous comment. I am generating the signal from -fs/4 to fs/4 & giving a shift of fs/4 so that my total signal now occupies the band from 0 to fs/2. Now, i'll not get any aliasing no? Also a further question, as i increase M, i will have to squeeze my signals into 0-fs/M no? Like for M=4, from 0 to fs/4. So am i not wasting the rest 3fs/4 band. Jun 28 '13 at 3:28