How to build a amplitude modulated tone?

Hello,

I would like to program a Amplitude modulated tone according to the formula:

stim = sqrt(2) * LvPa_ipsi * SoundEnv.*Carri_ipsi.*[2.*m.*(((1-cos(2.*pi.*fm))./2).^n-0.5)+1];

Since I am not an expert into math and signal processing, I only get an array of zeros. This formula will come in the last line before plotting. Can someone help me finding the bug in the code?

Best,

Paul

Here is my Code:

%% simulation parameters

clear

close all

clc

% stimulus sound parameters

Fq_ipsi = 2000; % [Hz] low-frequency stimulation

LvdB_ipsi = 80; % sound level [dBSPL]

LvPa_ipsi = 10^(LvdB_ipsi/20)*20e-6; % [Pa] calculated from dB SPL re 20 µPa

phase_ipsi = 0; % [rad] initial phase

Fq_contra = 2000; % [Hz] high-frequency stimulation

LvdB_contra = 80; % sound level [dBSPL]

LvPa_contra = 10^(LvdB_contra/20)*20e-6; % [Pa] calculated from dB SPL re 20 µPa

phase_contra = 0; % [rad] initial phase

% time steps

DTms = 0.01; % [ms] time step -- 100kHz sampling rate

% time lengths

Tall = 50; % [ms] entire duration of simulation

Tinit = 15; % [ms] starting time of stimulus

Tstim = 25; % [ms] duration of entire stimulus

Tramp = 3.9;% [ms] duration of stimulus ramp

Tlast = 10; % [ms] time after stimulus

Nall = round(Tall /DTms);

Ninit = round(Tinit/DTms);

Nstim = round(Tstim/DTms);

Nramp = round(Tramp/DTms);

Nlast = round(Tlast/DTms);

tvms = (0:Nall-1)*DTms-Tinit; % time vector (stimulus starts at time zero)

lmain = logical( [zeros(1,Ninit),ones(1,Nstim),zeros(1,Nlast)] );

% constructing sound stimuli

disp('Making sound stimuli');

% stimulus sound envelope (ramp)

SoundEnv = zeros(1,Nall);

% SoundEnv(Ninit+1 :Ninit+Nramp+1) = (0:Nramp)/Nramp; % upward ramp

SoundEnv(Ninit+1 :Ninit+Nstim+1) = 1; % stimulus

% SoundEnv(Ninit+Nstim-Nramp+1:Ninit+Nstim+1) = (Nramp:-1:0)/Nramp; % downward ramp

% Set-up for Amplitde modulated tone

fm = 128; % modulation frequency [Hz]

n = 1; % exponent

m = 1; % modulation depth

% stimulus sound waveforms

Carri_ipsi = sin( 2 * pi * Fq_ipsi * ((tvms-Tinit)/1000) + phase_ipsi); % carrier sine wave

Carri_contra = sin( 2 * pi * Fq_contra * ((tvms-Tinit)/1000) + phase_contra); % carrier sine wave

Sound_ipsi = sqrt(2) * LvPa_ipsi * SoundEnv .* Carri_ipsi; % apply ramp and scale to Pa

Sound_contra = sqrt(2) * LvPa_contra * SoundEnv .* Carri_contra; % apply ramp and scale to Pa

% Make the Signal Amplitude modulated tone

stim = sqrt(2) * LvPa_ipsi * SoundEnv.*Carri_ipsi.*[2.*m.*(((1-cos(2.*pi.*fm))./2).^n-0.5)+1];

figure()

subplot(2,1,1)

plot(tvms, stim)

subplot(2,1,2)

plot(tvms, Sound_contra)

title('Carrier')

xlabel ('Time / ms')

ylabel('Amplitude')

[Star Strider]

If the Signal Processing Toolboox is available, the modulate function makes this relatively straightforward.

.

Answer 1

[Ashutosh Singh Baghel]

Hi Paul,

I understand you are trying to implement Amplitude modulation. The BODMAS rule states we should calculate the Brackets first, then the Orders, then any Division or Multiplication, and finally any Addition or Subtraction. Here also,

stim = sqrt(2) * LvPa_ipsi * SoundEnv.*Carri_ipsi.*[2.*m.*(((1-cos(2.*pi.*fm))./2).^n-0.5)+1];

Here, the last term "2.*m.*(((1-cos(2.*pi.*fm))./2).^n-0.5)" is equal to -1 . So when +1 is added, this sums up to 0. Thats the reason for getting 'stim' signal as zero overall.

By simply adding a brackets in this line of code as follows, will solve the issue.

stim = sqrt(2) * LvPa_ipsi * SoundEnv.*Carri_ipsi.*[2.*m.*((((1-cos(2.*pi.*fm))./2).^n-0.5)+1)];

For more reference, go to MATLAB Documentation for 'amplitude modulation'.