sine wave that slowly ramps up frequency from f1 to f2 for a given time
algorithm, c, c++, math, waveform
Solution
if you want angular frequency (w=2 pi f) to vary linearly with time then `dw/dt = a` and `w = w0 + (wn-w0)*t/tn` (where `t` goes from 0 to `tn`, `w` goes from `w0` to `wn`). phase is the integral of that, so `phase = w0 t + (wn-w0)*t^2/(2tn)` (as oli says):
void sweep(double f_start, double f_end, double interval, int n_steps) {
for (int i = 0; i < n_steps; ++i) {
double delta = i / (float)n_steps;
double t = interval * delta;
double phase = 2 * PI * t * (f_start + (f_end - f_start) * delta / 2);
while (phase > 2 * PI) phase -= 2 * PI; // optional
printf("%f %f %f", t, phase * 180 / PI, 3 * sin(phase));
}
}
(where interval is tn and delta is t/tn).
here's the output for the equivalent python code (1-10Hz over 5 seconds):
from math import pi, sin
def sweep(f_start, f_end, interval, n_steps):
for i in range(n_steps):
delta = i / float(n_steps)
t = interval * delta
phase = 2 * pi * t * (f_start + (f_end - f_start) * delta / 2)
print t, phase * 180 / pi, 3 * sin(phase)
sweep(1, 10, 5, 1000)
ps incidentally, if you're listening to this (or looking at it - anything that involves human perception) i suspect you don't want a linear increase, but an exponential one. but that's a different question...
Problem
I'm writing a c program to generate a sinusoidal wave that slowly ramps up frequency from f1 to f2 for a giving time interval. I have written this c program to ramp the frequency from 0 to 10 Hz but the problem is that the frequency changes after completion of 360 degrees. If I try to change the frequency between 0 and 360 degree that the transition is not smooth and it is abrupt. This is the equation the sin that I have used y = Amplitude*sin(freq*phase) ``` int main(int argc, char *argv[]) { double y, freq,phase; int count; // for convenience of plotting in matlab so all the waves are spread on x axis. for (freq = 0; freq < 10; freq+=1) { for (phase = 0; phase < 360; phase++) { // phase is 360 degrees y = 3 * sin((count*6.283185)+(freq*(phase*(3.14159/180)))); printf("%f %f %f \n", freq, phase, y); } count++; } return EXIT_SUCCESS; } ``` - How do I change frequency smoothly for a given time period? - should I be looking into Fourier transformations?