The Fourier series expresses a periodic signal as a combination of sinusoidal waves, meaning the signal is made up of a combination of sine waves. The Fourier transform is a formula that transforms a signal recorded in time or space into its frequency components. It can process out noise from a signal to reveal the underlying frequencies, making the Fourier transform very good at filtering noise. The Fourier transform can operate on a function of either time f(t) or space f(x).

1. Discussion Reply Fourier Transform (Fourier series):
The Fourier series is used to express a periodic signal as a combination of sinusoidal waves,
meaning that we have a resultant signal that is made up of a combination of those sine
waves. The Fourier transform is a formula that is used to transform a signal that
was recorded in either time or space to the same signal sampled in the temporal or spatial
frequency. Using this we can help find the frequency components of these signals. In real
applications, signals can be muddied with noise which can hide their frequency
components. The Fourier transform can process out that extra noise to reveal
the frequencies thus making the Fourier series very good at filtering noise. The Fourier
Transform can either be f(t) for time or f(x) for time. ω = angular frequency and is to
frequency by The units for frequency are usually in Hertz(Hz). k = wavenumber, it has
units of inverse length and is to wavelength by References: Washington, A. J., & Evans, R.
(2017). Basic Technical Mathematics with Calculus (11th ed.). Pearson Education (US).
https://ecpi.vitalsource.com/books/9780134507095 Links to an external site.