I am unable to view the low frequency components of a signal that contains low (of the order of 20 KHz) and very high (of the order of THz) apart intermediate frequencies.

Hello. I am basically carrying out modulation of an optical signal (193.5 THz) by an RF signal (of the order of 10 GHz) and the modulated signal is again modulated by an NRZ representation of PRBS (approximately 20 KHz). The sampling frequency that I have used is 30 times the highest frequency, i.e., 30 * 193.5 THz. Mathematically the frequency components in the signal are 20 KHz, 10 GHz, 60 Ghz, 70 GHz and approximately 400 THz. When I carry out the FFT I noticed in the resulting plot that only the signal from 10 KHz onwards are visible. Is this because of the extremely high frequency components. (I tried a simple code starting off with a signal with two frequencies very close and then increasing one of them and observed that the higher order component in the FFT plot is distinct while the lower frequency component flattens out).

To view the low frequency, I designed a low pass FIR filter and used the filter to extract the 20 KHz signal but no avail. To verify if I was correct I tried extracting the 60 GHz and 70 GHz signal using a band pass FIR filter but noticed that although the 400 THz signal was suppressed the 10 GHz signal was intact. Is there any limitation in MATLAB or am I grossly wrong?

Thanks a million.

Answer 1

[Honglei Chen]

Without looking at your concrete steps, it's hard to judge. I'm also a bit confused when you say the signal from 10kHz onward is present, do you mean 10 GHz instead? Anyway, how many points are you using to do FFT? With your sample rate that high, if you don't have a lot of points, I doubt you'll be able to see anything in kHz range.

[Parikhit Dutta]

I do have a 20 KHz component in my signal. Basically it is a NRZ signal obtained from a PRBS 2^12 - 1 with a data rate of 1 Gbps. The fundamental frequency of this signal is approximately 20 KHz.

Basically the steps I carried out are summarized here.

1. An RF signal (10 GHz) is used to independently modulate two Laser source (1550 nm, 193.5 THz) that results in even and order order harmonics.

2. From the above modulated signal, the 4th order harmonic was modulated by a PRBS signal.

3. Then I use the 2nd, 3rd and 4th harmonic components as the input to my demodulator, necessarily a square law device.

4. The components I obtain are a DC component, 20 KHz, 10 GHz, 60 GHz, 70 GHz and 2*193.5 THz mathematically.

5. When I carried out an FFT of the signal I am unable to view any component below 10^8 Hz.

6. The number of points I have used in my FFT is 25000000 and my sampling frequency is 30*193.5 THz.

Hope that helps. If I increase the sampling frequency I run into 'Out of Memory'. In order to circumvent this I tried using an FIR filter to independently view the individual components.

1. A BPF with cut-off frequencies at 55 GHz and 75 GHz suppresses the higher components but doesn't suppress the 10 GHz component.

2. The sampling frequency for the filter is yet again 30 * 193.5 THz.

Is is possible to view such a varied group of frequencies in MATLAB? Am I wrong in my assumptions?

[Honglei Chen]

So you have a sample rate of 30*193.5 THz and your number of points is 25 million. This means that each point in your spectrum represents 30*193.5 THz/25e6 = 232.2 MHz. Therefore, you cannot see much of the 20 KHz. I would suggest you to do downsampling first if you really want to see something that low compared to your sampling rate.

As to the filter, I need a little more info. How are you designing the filter?

HTH