Howtosignalprocessing
Yes spectral leakage includes both negative and positive frequencies; i.e, the convolution is from −π to π.
- What is meant by spectral leakage?
- What are negative frequencies in spectrum?
- Can you have negative frequencies?
- What causes spectral leakage?
What is meant by spectral leakage?
Leakage, more explicitly called spectral leakage, is a smearing of power across a frequency spectrum that occurs when the signal being measured is not periodic in the sample interval.
What are negative frequencies in spectrum?
Negative frequency is an idea associated with complex exponentials. A single sine wave can be broken down into two complex exponentials ('spinning numbers'), one with a positive exponent and one with a negative exponent. That one with the negative exponent is where you get the concept of a negative frequency.
Can you have negative frequencies?
In real world, the negative frequency does not exists and the spectral content on negative frequencies must be added to the spectral content at the positive frequencies, to save energy. The concept of negative frequencies is used broad wide namely in this sense, in the connection with complex numbers.
What causes spectral leakage?
Spectral leakage results from an assumption in the fast Fourier transform (FFT) and discrete Fourier transform (DFT) algorithms that the time record exactly repeats throughout all time. Thus, signals in a time record are periodic at intervals that correspond to the length of the time record.
