If X1(k) and X2(k) are the N-point DFTs of X1(n) and x2(n) respectively, then what is the N-point DFT of x(n)=ax1(n)+bx2(n)?

Discrete Fourier Transform – Properties and Applications topics include: Discrete fourier transforms, their sampling and properties, linear filtering methods on DFT and their frequency analysis. The discrete Fourier transform (DFT) is a mathematical function that converts a sequence of equally-spaced samples of a function into a sequence of equally-spaced samples of the discrete-time Fourier transform. The DFT is a frequency domain representation of the original input sequence.  The DFT is used in engineering to convert a signal from the time domain into the frequency domain. This helps... Show more

Discrete Fourier Transform – Properties and Applications topics include: Discrete fourier transforms, their sampling and properties, linear filtering methods on DFT and their frequency analysis.

The discrete Fourier transform (DFT) is a mathematical function that converts a sequence of equally-spaced samples of a function into a sequence of equally-spaced samples of the discrete-time Fourier transform. The DFT is a frequency domain representation of the original input sequence. 

The DFT is used in engineering to convert a signal from the time domain into the frequency domain. This helps analyze the frequency components of the signal. The DFT is the core of many digital signal processing systems. 
The DFT has the following properties: Linearity, Time shifting, Time modulation, Multiplication. 
The basis functions of the DFT are a set of sine and cosine waves with unity amplitude.

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