# Tagged Questions

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### Is there a way to modify the exponential smoothing function to account for varying sample rates?

I am using a simple exponential smoothing formula to smooth a signal. X(n) = a * S(n) + ( 1 - a ) * X(n-1) However on certain setups, the sample rate is much ...
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### A relationship among multiple periodic arrays

There are N periodic arrays ai[n] with period Ti, respectively, where i=1, 2, … , N. Each array has a property that a[n]=1 when n=k*T where k is integer, otherwise a[n]=0. Then a new array is created ...
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### How do we determine the duration of a fundamental frequency using the DFT (or FFT)?

I'm still in the process of learning the details of the DFT (and FFT) and I've just made a test .wav file in Audacity by joining 3 one-second sine waves together. .wav file 1 = 440 Hz, sample rate ...
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### How do I deal with a seemingly fractional delays in discrete time fourier transforms?

Is a transfer function of a discrete time system is $H(e^{j\Omega})=e^{-j\Omega/4}$ and I feed it an impulse, what will be it's response? I know that technically a transfer function of ...
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### Continuous time signal and Discrete time signal

I know that all periodic continuous time signal have discrete spectral representations, but are all discrete spectral representations periodic in continuous time? Also, can all periodic signals be ...
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### Autocorrelation of the rectangular function

Given the autocorrelation function of the signal "s": $$r(k)=\sum_{t=-\infty}^{+\infty}{s(t)\cdot s(t+k)}$$ The autocorrelation of a rectangular function $\Pi$ (t/2) is a triangle formed by the ...
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### How do I find transfer function of a discrete-time system when its state-space form is given?

I read this and this Wikipedia pages, but both of them are explaining continuous-time systems. My question is about discrete-time case. For example, given the state-space equations of the second ...
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### solve an difference equation's particular solution with unit step input

I have a question like this $y[n] - \frac 2 5y[n-1] = 2x[n]$ and $x[n] = 2u[n]$, the manual say that $y^p[n] = k u[n]$ and subtitute it into the equation will become $k - \frac 25k = 4$. But I think ...
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### Finding two highest peaks in a chunk of samples

Supose I have a list of 600 samples of numbers, and the histogram of the samples looks like the following: As can be seen, there are two 'mountains' of values around 16 and 48, and a outlier in 95. ...