I am relatively new to DSP and have been reading a lot on the internet. I have a couple of questions.

I have a signal in the form of a function $$ f(x) = A_0 + A_1 \cos(\omega_1 x) + A_2 \cos(\omega_2 x)+...+ A_n \cos(\omega_n x). $$ I have $f(x)$ and I know the minimum and maximum frequencies. $f(x)$ can have really high frequencies.

a) I need to find the amplitude $A_p$ of a particular frequency $\omega_p$ in $f(x)$. One way to do this is, I could get sample points from $f(x)$ sampling at greater than Nyquist rate and do an FFT and find the amplitude. But if $f(x)$ has really high frequencies, the sampling would take most of the time. If i am interested only in estimating the amplitude $A_p$, is there another way, a faster way, of doing this. In the best case, I would like to estimate $A_p$ to within 0.5 of its actual value.

b)If I want $A_0$, the DC component, I can compute the average of $f(x)$ but with high frequencies in $f(x)$ that would mean high sampling rates. Any other faster way of doing this?

c)The FFT takes $O(n\log(n))$ if $n$ is the size of the input and returns the magnitudes for $n$ different frequencies. If we are only interested in one particular frequency we should be able to alter the source code so that it would take only $O(\log(n))$, right?

Thanks for answering!


2 Answers 2


The usual way to estimate the amplitude of a particular frequency is to use the Goertzel algorithm. There is a good write-up by Rick Lyons here.

Even though Rick's writeup is about single tone detection, it can be applied when multiple tones are present, too.

  • 1
    $\begingroup$ Unless they are close relative to the observation time. Then the estimation isn't good. $\endgroup$
    – Royi
    Commented Jun 19, 2018 at 11:57

Maybe you have a look at Goertzels Algorithm.

  • 1
    $\begingroup$ Beat me to it! :-) +1 $\endgroup$
    – Peter K.
    Commented Jan 8, 2014 at 18:20
  • 2
    $\begingroup$ OP states that he only knows the bounds of the frequencies w1...wn, not the individual values. Goertzel requires knowing the frequency wp. Is it known? $\endgroup$
    – John
    Commented Jan 8, 2014 at 18:58
  • 1
    $\begingroup$ @John : Good point! I missed that piece. :-( $\endgroup$
    – Peter K.
    Commented Jan 8, 2014 at 19:00
  • 1
    $\begingroup$ yes, i know w1, wp and wn $\endgroup$
    – user7502
    Commented Jan 8, 2014 at 19:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.