Total energy in Time and Frequency Dimain

I truly appreciated if somebody can direct me how to measure total energy in a certain frequency band?

I have a signal and use this code to measure total enery and the result is reasonable.

E1_timedomain=sum(abs(x.^2))

but it measuers total energy of whole signal. I just want to measure it between [0-100] Hz. Appreciared!

Answer 1

[Star Strider]

If you have R2018a or later, and the Signal Processing Toolbox, use the bandpass function to selectively filter the frequencies-of-interest. Then do whatever calculations you want to do on the output. If you have an earlier version, it is easy to design filters in MATLAB. I will help you with that, if necessary.

[Maria Amr]

Star Strider Thank you so much.

As usual, the best and the fast way.BIG like!

[Star Strider]

As always, my pleasure!

Answer 2

[Maria Amr]

Star Strider I have applied a bandpass filter and get a reasonable result. Would you please direct me how may I retrive the filtered signal? Appreciated!

that is my code:

bandpass(amp1,[1 78],fs);

[Star Strider]

You need to use an output:

filtered_signal = bandpass(amp1,[1 78],fs);

Answer 3

[Maria Amr]

Star Strider Appreciated!

[Star Strider]

As always, my pleaure!

(Also, in the future please post comments as Comments, not Answers.)

Answer 4

[Paul]

Define a real-valued, finite duration signal of length N, assumed to be uniformly spaced samples collected as Fs = 2000 Hz

rng(100);
N = 1000;
x = randn(1,N); Fs = 2000; Ts = 1/Fs;

The total energy in this signal is computed in the time domain as

E = sum(abs(x).^2)

E = 1.0063e+03

The total energy computed in the frequency domain is (taking advantage of the symmetry in the frequency domain because x is real-valued)

X = @(f) freqz(x,1,f,Fs);
E = 2*integral(@(f) abs(X(f)).^2,0,Fs/2)*Ts

E = 1.0063e+03

Hence, the energy in the signal between 0-100 Hz is

E100 = 2*integral(@(f) abs(X(f)).^2,0,100)*Ts

E100 = 95.8129

Can also approximate E100 from the DFT samples.

Xdft = fft(x);
fdft = (0:N-1)/N*Fs;
E100 = 2*sum(abs(Xdft(fdft<=100)).^2)/N

E100 = 99.5646

Or better yet

E100 = 2*trapz(fdft(fdft<=100),abs(Xdft(fdft<=100)).^2)/Fs

E100 = 94.7997

Can also apply a very sharp, low pass filter to x and then compute the energy in the filter output as a rough approximation

y = lowpass(x,100,Fs,'Steepness',0.95);
sum(abs(y).^2)

ans = 112.4906