Communications Toolbox

Significance of Sampling Rates

The vectors and matrices that form the input and output of the modulation and demodulation functions do not have a built-in notion of time. That is, MATLAB does not know whether the digital signal [0 1 2 3 4 5 6 7] represents an 8-second signal sampled once per second, or a 1-second signal sampled eight times, or something else. However, many functions appearing in this Modulation section ask for one or more sampling rates. This subsection discusses the significance of these sampling rates.

If your application has a natural notion of time, then you are free to use it in the modulation and demodulation functions. For example, if you generate the digital signal [0 1 2 3 4 5 6 7] and know that it represents a 1-second signal sampled eight times, then set Fd = 8. On the other hand, if you know that the signal represents a 2-second signal sampled four times per second, then set Fd = 4. You can also use the formula

• Fd = size(x,1) / (max(t)-min(t)); % if x=signal, t=sample times
  

for a signal x sampled at times t. Here x is a matrix or vector and t is a vector whose length is the number of rows of x.

For most digital modulation computations, MATLAB does not directly use the sampling rates Fd and Fs of digital message signals and mapped signals, respectively. What it uses is their ratio Fs/Fd. For example, the two commands below produce exactly the same result, because 3/1 equals 6/2.

• y13 = dmodce([0 1 2 3 4 5 6 7]',1,3,'ask',8);
  y26 = dmodce([0 1 2 3 4 5 6 7]',2,6,'ask',8);
  

One exceptional situation in which the individual value of Fd matters occurs in the MSK and M-ary FSK methods. The default separations between successive frequencies are Fd/2 and Fd for these two methods, respectively.

Choosing Sampling Rates for Passband FSK Modulation

If you use the dmod and ddemod functions to perform passband FSK modulation, then your choice of the Fc, Fd, and Fs parameters influences the accuracy of the results. The table below lists suggested minimum values for small alphabets. The minimum values yield performance results that match theoretical data to within 0.1 dB when tested using an AWGN channel. To get closer to theoretical data, you should use values of Fc and Fs that exceed the minimum values listed in the table.

Alphabet Size, M	Carrier Frequency, Fc	Sampling Rate of Unmodulated Data, Fd	Sampling Rate of Modulated Data, Fs
2	8	1	8*Fc
4	16	1	8*Fc
8	32	1	8*Fc
16	64	1	8*Fc

Representing Digital Signals

Representing Signal Constellations