Linked Questions

13 votes
9 answers
3k views

Estimate Sine Frequency under White Noise — simple and effective method

Given a sinusoidal signal in white noise, how can one efficiently determine its frequency?
RyanRonald's user avatar
9 votes
3 answers
8k views

Extract Sine Phase and Amplitude - accurate and robust method

This is a followup question to one I asked earlier based on the chat after the answer given by @hotpaw2, and cross-posted from stackoverflow since it was suggested it is more relevant to DSP. I have a ...
KBriggs's user avatar
  • 320
5 votes
9 answers
887 views

How Do I Measure the Time Duration of a Finite Length Discrete Sequence?

Assume I have a five-sample time-domain sequence (none of the five samples are zero valued) and the time period between each pair of samples is one second. Measured in seconds, what is the time ...
knight's user avatar
  • 77
8 votes
5 answers
1k views

Estimation of Amplitude, Frequency and Phase of Linear Combination of Harmonic Signal Beyond the Leakage Resolution of DFT

How can I find a rough ( as accurate as possible) Amplitude of each frequency when there is spectral leakage. Currently, I am dealing with a system that contains special leakage which seems ...
Jacob wood's user avatar
4 votes
2 answers
921 views

How does the effect of windowing change with the phase of the input signal?

I am calculating the SNR (signal power to noise power) for a sine wave. I don't have an integer number of periods in the waveform being analyzed, so I am using a flattop window to reduce spectral ...
DavidG25's user avatar
  • 119
1 vote
2 answers
568 views

How can I solve such an inverse Z-transform?

I was going through some old exams and found this question: Find the inverse $Z$-transform of $z^{-1/2}$. I tried using the properties table, but I couldn't find a single useful property that would ...
user avatar
2 votes
2 answers
413 views

The uncertainty principle - Why does it imply that we can't localise

The uncertainty principle states that if you have a signal which is very concentrated in time, then its Fourier transform will be rather outspread and vice versa. However, I don't really understand ...
Richard's user avatar
  • 129
4 votes
3 answers
127 views

Algorithm for finding best matching sin wave to input signal

Question Suppose I take a signal $y(t) = \cos(2\pi \cdot 4.1t + 2)$ and I sample it uniformly up to 2 seconds. Given only these time samples, how would I design an algorithm that finds the pair of ...
GlitchesEtcEtc's user avatar
0 votes
1 answer
111 views

Unwindowed STFT of sine, closed form solution and insights (sliding FFT)

I seek to calculate, mathematically, the unwindowed Short-Time Fourier Transform of $$ \cos(2\pi f t + \phi) $$ i.e. any arbitrary real-valued sine: any frequency, duration, phase shift, and number of ...
OverLordGoldDragon's user avatar
0 votes
2 answers
96 views

DFT modulus of a sine, closed form solution and insights

A closed form solution to $$ X[k] = \texttt{DFT}\{\cos(2\pi f t + \phi)\} $$ confirmed many known properties of a finite sine's spectrum, also revealed new ones. Can the same be done for $|X|$, or $|X|...
OverLordGoldDragon's user avatar
0 votes
1 answer
80 views

Effect of sampling rate and duration on discrete parameters of sine (spectrum)?

The DFT of $$ \cos(2\pi f t + \phi) $$ peaks at $k=\pm f$ if $t = \frac{1}{N}[0, 1, ..., N - 1]$ (for integer $f$, & within Nyquist). What about other $t$? What if we double the sampling rate or ...
OverLordGoldDragon's user avatar