```
function s = sig_linsweep(fs, N, range)
%sig_linsweep Create a linear frequency sweep with constant magnitude spectrum
% Usage: s = sig_linsweep(fs, N, range)
%
% S = sig_linsweep(FS, N) returns a sweep of length N with normalized
% amplitude and sampling rate FS with a perfectly constant magnitude
% spectrum. It covers all frequencies from 0 to FS/2 and runs from
% the first to the last sample.
%
% S = sig_linsweep(FS, N, RANGE) returns a sweep of length N with
% normalized amplitude and a sampling rate of FS and a perfectly
% constant magnitude spectrum. The signal covers all frequencies
% from 0 to FS/2. The sweep starts at sample RANGE(1)
% and ends at sample RANGE(2), i.e., RANGE must be an array
% with two positive elements with 0 < RANGE(1) < RANGE(2) <= N.
% A tail is encountered before and after the actual sweep range.
%
% EXAMPLE 1: Create a perfect sweep and display its spectrogram:
%
% fs = 44100; % sampling rate of 44100 Hz
% s = sig_linsweep(fs, 4*fs) % 4 secs sweep
% spectrogram(s, 256, 128, 256, fs, 'yaxis');
% sound(s,fs);
%
% EXAMPLE 2: Create a perfect sweep in a range:
%
% fs = 44100; % sampling rate of 44100 Hz
% s = sig_linsweep(fs, 4*fs, [fs+1,2*fs]); % 4 secs with sweep
% % from fs+1 to 2*fs
% spectrogram(s, 256, 128, 256, fs, 'yaxis');
% sound(s,fs);
%
% To create a continuous measurement stimulus, you have to stack as
% many length N periods together as you need. Considering the sampling
% rate fs, you have to repeat the sweep period t*fs/N times to get a
% signal length of t seconds. Make sure t*fs/N is an integer.
%
% Url: http://amtoolbox.org/amt-1.1.0/doc/signals/sig_linsweep.php
% Copyright (C) 2009-2021 Piotr Majdak, Clara Hollomey, and the AMT team.
% This file is part of Auditory Modeling Toolbox (AMT) version 1.1.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% Author: Aulis Telle, IND, 2008
% Modifications: 11.07.2017, Piotr Majdak, documentation fix
if exist('range','var')
if length(range) ~= 2 ...
|| range(1) > range(2) ...
|| range(1) < 1 ...
|| range(2) > N
error('RANGE must be an array with two elements 0 < RANGE(1) < RANGE(2) <= N.');
end
else
range = [1 N];
end
% initialization
isEven = (mod(N,2) == 0);
Nhalf = ceil(N/2);
ph = zeros(1, N);
% The group delay (in seconds) of every frequency bin is
% the index of the frequency bin divided by half of the
% sampling frequency. This way the frequency corresponding to
% frequency index k occurs at time index 2*k.
groupDelay = ((0:Nhalf-1) / N * range(2) + range(1) - 1) / (fs/2);
% Width of a frequency bin (in radians)
deltaOmega = 2 * pi * fs / N;
% The phase is calculated by integrating over the linear
% group delay, i.e., the value of the group delay times the
% current frequency divided by two (because we have a
% triangular area under the groupDelay curve).
ph(1:Nhalf) = - groupDelay .* (deltaOmega * (0:length(groupDelay)-1))./2;
% Construct an odd-symetrical phase needed for a real valued signal
% in time domain.
if isEven
ph(Nhalf+1:end) = [0 -fliplr(ph(2:Nhalf))];
else
ph(Nhalf+1:end) = -fliplr(ph(2:Nhalf));
end
% Calculate complex represenation with constant magnitude for IFFT
c = 10*exp(i*ph);
% Calculate IFFT to gain sweep signal in time domain
s = real(ifft(c));
% Normalize signal to have a maximal amplitude of one
s = s / max(abs(s));
```