Why does Fourier transform have negative frequency?
Negative frequency doesn’t make much sense for sinusoids, but the Fourier transform doesn’t break up a signal into sinusoids, it breaks it up into complex exponentials. The meaning of negative frequencies is just mathematical(not physical) similarly to the imaginary part of a complex signal.
How is a negative frequency different from a positive frequency?
Negative frequency is no different from the above simple example. A simple mathematical explanation of how the negative frequency pops up can be seen from the Fourier transforms of pure tone sinusoids. Consider the Fourier transform pair of a complex sinusoid: e ȷ ω 0 t ⟷ δ ( ω + ω 0) (ignoring constant multiplier terms).
Why do you have two frequency components in the FFT?
An easy way of thinking about the problem is to imaging a standing wave. The standing wave (in time domain) can be represented as a sum of two oppositely moving traveling waves (in frequency domain with positive and negative k vector, or +w and -w which is equivalent). Here comes the answer on why you have two frequency components in the FFT.
Can a Fourier transform produce a negative frequency?
The Fourier Transform uses a complex exponential as its basis function and applied to a single real-valued sine wave happens to produces a two valued results which is interpreted as positive and negative frequency. There are other transforms (like the Discrete Cosine Transform) which would not produce any negative frequencies at all.
Is the negative part of the frequency axis redundant?
On the ‘complex exponential frequency axis’, for real signals, it is well known that the negative frequency part is redundant and only the positive ‘complex exponential frequency axis’ is considered. In making this step implicitly we know that the frequency axis represents complex exponential repetition and not sinusoidal repetition.