Sweep / chirp signal ends at incorrect frequency

Question

I'm creating a sweep / chirp signal using matlab / octave and my ending signal seems to be ending at the wrong frequency. How can I fix it so that the signal ends at the correct frequency.

PS: I can't use the chirp command in octave because I'm creating a chirp / sweep signal using a specific equation.

Example code with simple equation. and plot of problem

%test sweep / chirp

clear all,clc
freq1=20; %start freq
freq2=200; %end freq
fs=44100;
dur=1; %duration of signal in seconds

t = linspace(0,2*pi,fs*dur);

f=freq1:(freq2-freq1)/length(t):freq2-(freq2-freq1)/length(t); 
%20:(200-20)/lenght(t) :200-(200-20)/length(t)

data=sin(f.*t); %build signal
data=(data/max(abs(data))*.8); %normalize signal
wavwrite([data'] ,fs,32,strcat('/tmp/del.wav')); %export file
plot(t,data)

PS: I'm using octave 3.8.1

Answer 1

The following code explains how to generate a frequency-variable sin wave.

freq1=20; %start freq
freq2=200; %end freq
dur=1; %duration of signal in seconds


freq=@(t)freq1+(freq2-freq1)/dur*t;
%another example, may help to understand the code
%dur=2
%freq=@(t)heaviside(t-1)*10+heaviside(t-1.5)*-9;
%Integerate over the time-local frequency, gives the average frequency until t which later on gives the sin with the right phase
%In case you don't have symbolic toolbox, integrate manually. For the given numbers Ifreq=@(x)x.*(x.*9.0+2.0)
Ifreq=matlabFunction(int(freq(sym('x'))));
%Defining wave function based on `Ifreq`
wave=@(t)(sin(Ifreq(t)*2*pi));
t=0:.00001:dur;
plot(t,wave(t));

Answer 2

Following Daniel's recipe, this is a version that uses numerical integration, and consequently doesn't require the symbolic toolbox:

freq1 = 20;  % start frequency
freq2 = 200; % end frequency
fs = 44100;
dur = 1;     % duration of signal in seconds

t = 0:1/fs:dur;
freqt = linspace(freq1,freq2,numel(t));
ifreqt = cumsum(freqt)/fs;
data = sin(2*pi*ifreqt);
plot(t,data);