Issue with generating a sine wave via linspace and colon

Hi Everyone, I'm having an issue with generating a sine wave using the linspace operator vs colon operator. The code is below:

%% Generate a sinusoidal wave
fc = 300e6; % center frequency
duration = 5e-3; % Total duration
fs = 10e6; % Sampling Rate
N = fs * duration; % Total number of samples
% Method 1, using linspace
t1 = linspace(0,duration,N);
% Method 2, using colon
t = 0:1/fs:duration;
% Plotting both of them
x1=sin(2*pi*fc*t1); x = sin(2*pi*fc*t);
figure;
subplot(211)
plot(t1,x1)
subplot(212)
plot(t,x)

Running this Code gives a very different result for the colon operator as can be seen clearly. Obviously I can just use the linspace function, but the main issue I have is that I'm trying to generate the sine wave in C++, and in there there's no linspace equivalent, and I'm using getting the same output as shown in the 2nd image. Hence I'm trying to debug this issue in MATLAB first.

From what I can tell, the two time variables are mostly identical, but differ in maybe 5th-6th decimal place, which shouldn't be enough to cause such massive discrepency. If anyone can help that'd be appreciated.

[Dyuman Joshi]

> "From what I can tell, the two time variables are mostly identical"

No.

linspace(x1,x2,N) generates n points with spacing (x2-x1)/(N-1), which in your case is duration/(N-1) and the spacing for colon is 1/fs, which is equal to duration/N (from the definition of N). Different spacing means the resulting vectors will not be same/similar.

To make them identical theoretically, use N+1 points with linspace

Also, Use sinpi(x) instead of sin(pi*x) as it is more accurate - sinpi

Answer 1

[DGM]

You're trying to draw a sine wave with a frequency 30x higher than your sampling rate. The output is nothing but aliased nonsense in both cases. If you make t1 have N-1 samples, you'll see that the illusory sine wave disappears. Neither output is good.

Make some adjustments:

% Generate a sinusoidal wave
fc = 300e6; % center frequency
duration = 50e-9; % Total duration (short enough to be viewable)
fs = 10e9; % Sampling Rate (high enough to produce meaningful output)
N = fs * duration; % Total number of samples

% Method 1, using linspace
t1 = linspace(0,duration,N);
% Method 2, using colon
t2 = 0:1/fs:duration;
% Plotting both of them
x1 = sin(2*pi*fc*t1); 
x2 = sin(2*pi*fc*t2);

subplot(211)
plot(t1,x1)
subplot(212)
plot(t2,x2)

[Swapnil srivastava]

I overlooked the most obvious thing lol. Thanks a lot.

[Bruno Luong]

Make it

t1 = linspace(0,duration,N+1)

[DGM]

That too, yes. I wasn't really paying attention to the difference in vector length, but if you want equivalence ...