Assuming I have a signal x(t), would it be possible for me to detect the peak in the frequency spectrum (that is, the frequency with the highest energy content) without using FFTs ?
*PS - I saw something in Wavelet Decomposition called scale2freq(). I looked over that in the MATLAB help page and it ended up confusing me. Does the function have anything to do with frequency representations? If yes, how do I find peak frequencies using it?
What you probably want is called a pitch detection algorithm and there is a variety of them in time-domain or frequency-domain (or both of them). Please search google for "pitch detection algorithms" for further reference or check selected links for a quick overview:
In time-domain some simple approach is to locate peaks of autocorrelation function. Indeed autocorrelation is maximal at t=0 and then next peaks gives an estimation of the main period:
ncount = 10000;
Ts = 0.0001; % Sampling period
t = (1:ncount) * Ts; % Sampling times
f = sin(2*pi*60*t) + 0.1*sin(2*pi*200*t) + 0.01 * randn(1, length(t)); % Signal
R = xcorr(f);
[~, locs] = findpeaks(R);
meanLag = Ts * mean(diff(locs));
pitch = 1 / meanLag; ===> Will be around 60 Hz
This approach is ok for very basic signals, you'll probably have to refine it upon you situation (noise level, periodicity, multi-tone, etc...). See above references for more refined algorithms.
