Need Help running functions Resubmit

I am resubmitting this question again.

I need help coding and running some functions for the signal in the attached. I need to find the value of the signal bandwidth using the following bandwidth definitions:

(a) Half-power bandwidth.

(b) Null-to-null bandwidth.

(c) 99% of power bandwidth. (Hint: Use numerical methods.)

(d) Bandwidth beyond which the attenuation is 35 dB.

Below is what I have so far for the code but I get several errors when I try to run. Could you please help

clc
clear all
f=446000
Gx(f)=10^-4*(sin(pi*(f-10^6)*10^-4)/(pi*(f-10^6)*10^-4))

% calculate half-power beamwidth
function Bw = half_power_bw(f, Gf)
% Find the index of the maximum value in the magnitude spectrum
[~,imax] = max(abs(Gf));
% Find the indices of the half-power points
i_half_lower = find(abs(Gf) < abs(Gf(imax))/sqrt(2), 1, 'first');
i_half_upper = find(abs(Gf) < abs(Gf(imax))/sqrt(2), 1, 'last');
% Calculate the half-power bandwidth 
Bw = f(i_half_upper) - f(i_half_lower);
end

% null-to-null beamwidth
function Bw = null_to_null_bw(f, Gf)
% Find the first and last nulls of the magnitude spectrum
nulls = find(abs(Gf) == 0);
i_null_lower = nulls(1);
i_null_upper = nulls(end);
% Calculate the null-to-null bandwidth
Bw = f(i_null_upper) - f(i_null_lower);
end

% 99% of power beamwidth
function Bw = power_bw(f, Gf, power_fraction)
% Calculate the total power
total_power = trapz(f, abs(Gf).^2);
% Find the index where the cumulative power reaches the desired fraction
power_integral = cumtrapz(f, abs(Gf).^2);
i_power = find(power_integral >= total_power*power_fraction, 1, 'first');
% Calculate the bandwidth at the desired power fraction
Bw = f(i_power);
end

% Bandwidth beyond which the attenuation is 35 dB.
function Bw = attenuation_bw(f, Gf, attenuation_dB)
% Convert attenuation from dB to linear scale
attenuation_linear = 10^(-attenuation_dB/20);
% Find the index where the magnitude spectrum falls below the attenuation level
i_attenuation = find(abs(Gf) < abs(max(Gf))*attenuation_linear, 1, 'first');
% Calculate the bandwidth beyond the attenuation level
Bw = f(i_attenuation);
end

Answer 1

[Balavignesh]

Hello James,

I understand that you're looking to determine the bandwidth of a signal using various definitions. However, there are a few corrections needed in your code.

The signal `Gx` should be evaluated across a spectrum of frequencies, not solely at `f = 446000`. Therefore, the way `Gx(f)` is defined in your code does not align with MATLAB's syntax. You'll need to define `Gx` as an anonymous function or within a function file to cover the desired frequency range. Moreover, the `power_bw` function is intended to identify both the lower and upper frequency limits that encompass a specified percentage of the signal's power. Additionally, when calculating `null_to_null_bw`, searching for exact zeros in `Gf` may lead to inaccuracies due to the discrete nature of the data. It's more reliable to detect zero crossings by observing sign changes in `Gf`.

Below, I've provided a revised version of the code that addresses these issues and assists you in accurately calculating the bandwidth.

clc
clear all

% Define the frequency range
f = linspace(0, 2e6, 10000); % 0 to 2 MHz with 10000 points

% Define Gx as an anonymous function
Gx = @(f) 10^-4 * (sin(pi*(f-10^6)*10^-4) ./ (pi*(f-10^6)*10^-4));

% Evaluate Gx over the frequency range
Gf = Gx(f);

hp_bw = half_power_bw(f, Gf);
nn_bw = null_to_null_bw(f, Gf);
p99_bw = power_bw(f, Gf, 0.99);
att35_bw = attenuation_bw(f, Gf, 35);

% Display the results
fprintf('Half-power bandwidth: %f Hz\n', hp_bw);

Half-power bandwidth: 9000.900090 Hz

fprintf('Null-to-null bandwidth: %f Hz\n', nn_bw);

Null-to-null bandwidth: 1999799.979998 Hz

fprintf('99%% of power bandwidth: %f Hz\n', p99_bw);

99% of power bandwidth: 186818.681868 Hz

fprintf('Bandwidth beyond which the attenuation is 35 dB: %f Hz\n', att35_bw);

Bandwidth beyond which the attenuation is 35 dB: 0.000000 Hz

% Local function definitions:
function Bw = half_power_bw(f, Gf)
    [~,imax] = max(abs(Gf));
    i_half_lower = find(abs(Gf(1:imax)) < abs(Gf(imax))/sqrt(2), 1, 'last');
    i_half_upper = find(abs(Gf(imax:end)) < abs(Gf(imax))/sqrt(2), 1, 'first') + imax - 1;
    Bw = f(i_half_upper) - f(i_half_lower);
end

function Bw = null_to_null_bw(f, Gf)
    % Find sign changes in Gf which indicate a null has been crossed
    sign_changes = find(diff(sign(Gf)) ~= 0);
    % If there are no sign changes, then there are no nulls
    if isempty(sign_changes)
        Bw = 0;
        return;
    end
    % Assuming the first and last sign changes correspond to the first and last nulls
    i_null_lower = sign_changes(1);
    i_null_upper = sign_changes(end);
    % Calculate the null-to-null bandwidth
    Bw = f(i_null_upper) - f(i_null_lower);
end

function Bw = power_bw(f, Gf, power_fraction)
    total_power = trapz(f, abs(Gf).^2);
    power_integral = cumtrapz(f, abs(Gf).^2);
    lower_idx = find(power_integral >= total_power*(1-power_fraction)/2, 1, 'first');
    upper_idx = find(power_integral >= total_power*(1+power_fraction)/2, 1, 'first');
    Bw = f(upper_idx) - f(lower_idx);
end

function Bw = attenuation_bw(f, Gf, attenuation_dB)
    attenuation_linear = 10^(-attenuation_dB/20);
    i_attenuation = find(abs(Gf) < abs(max(Gf))*attenuation_linear, 1, 'first');
    Bw = f(i_attenuation);
end

Kindly have a look at the following documentation links to have more information on:

• 'functions' in MATLAB: https://www.mathworks.com/help/matlab/ref/function.html
• 'trapz' function: https://www.mathworks.com/help/matlab/ref/trapz.html

Hope this helps!

Balavignesh