Question

I have an array of bits, such as the one below, and I need to put a carrier wave on top of them. The question is: Is this possible to do without looping?

For example, suppose you are using Frequency-Shift-Keying. If the bit is a “1” then the signal should be a sine wave with a frequency of 10,000 Hz, and if the bit is a “0” then the signal should be a sine wave with a frequency of 8,000 Hz.

Bit-Array:

bits = [0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1]

Looping Code:

for i = 1:length(bits)
   if bits(i) == 1
      signal = [signal sin(2*pi*10000*t)]
   else
      signal = [signal sin(2*pi*8000*t)]
   end    
end

It would be nice if I could perform this all in a single operation with no looping.

Thanks.

Answer 1

If t is a scalar, then you can replace your for loop with a single-line vectorized solution:

signal = sin(2*pi*t.*(8000+2000.*bits));

However, if you’re doing frequency-shift keying, it seems like you should be expanding each 0 or 1 in your bits vector into a sine wave with a given duration and frequency. For example, to create a modulated signal with 4 sine periods (0.1 msec) at 8 kHz for each 0 and 5 sine periods (0.1 msec) at 10 kHz for each 1, you can use the function KRON like so:

t = 0:5e-6:4.95e-4;
signal = sin(2*pi.*(kron(bits,10000.*t)+kron(~bits,8000.*t)));