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Discrete Fourier Transform (DFT)
Discrete Fourier Transform (DFT)
Introduction
Signal time sampling. Discrete-Time Fourier Transform.
Signal time repetition. Discrete Fourier Transform
Inverse Discrete Fourier Transform
Conclusions
Reference
Indexing and shifting of Discrete Fourier Transform
Introduction
Indexing of DFT spectrum samples
DFT shifting
DFT shifting for even $N$
DFT shifting for odd $N$
DFT shifting example
Conclusions
Reference
Discrete Fourier Transform Properties
Introduction
DFT Linearity
DFT of Signal with Circular Shifting in Time
DFT of Signals Circular Convolution
DFT of Two Signals Cut Product
Property of the DFT Circular Shifting in Frequency
DFT Symmetry of a Real-Valued Signal
Spectrum Frequency Inversion of a Real-Valued Signal for Even $N$
The zero DFT sample
Duality Property
Conclusions
Reference
Calculating the Discrete Fourier Transform (DFT)
Fast Fourier Transform Introduction
Introduction
FFT Algorithm Development Principle
Inverse Fast Fourier Transform
Conclusions
Reference
Radix-2 Decimation in Time FFT Algorithm
Introduction
Initial Sequence Divide by Decimation in Time
Conquer Procedure
Butterfly Diagram
Full Diagram of Decimation in Time FFT Algorithm. Bit Reversal
Conclusions
References
Radix-2 Decimation in Frequency FFT Algorithm
Introduction
Decimation in Frequency FFT Algorithm
Butterfly Diagram of Decimation in Frequency FFT Algorithm
Complete Diagram of Decimation in Frequency FFT Algorithm
Conclusions
Reference
Goertzel Algorithm
Introduction
Recurrence relation to calculate the fixed signal spectral sample
Goertzel Algorithm
Example of Using Goertzel Algorithm
Using Goertzel Algorithm to Decode the DTMF signal
Conclusions
Reference
Digital sample-rate conversion
Digital resampling by using polynomial interpolation. Farrow filter
Introduction
Problem definition
Lagrange polynomial interpolation
Effective polynomial representation according to Horner structure
Using polynomial interpolation for digital signal resampling
Minimization of multipliers when calculating Lagrange polynomial interpolation
Conclusions
Reference
Using Farrow filter on the basis of piecewise and cubic polynomial interpolation for digital signal resampling
Introduction
Recalculating sample indexes of an input signal in case of piecewise and cubic interpolation
Using Farrow filter on the basis of polynomial interpolation to compensate the signal fractional delay
Using Farrow filter as a digital signal interpolator
Using Farrow filter for fractional change of the signal frequency sampling
Conclusions
Reference
Farrow Filter of Signal Digital Resampling on the Basis of Spline Interpolation
Introduction
Creating Cubic Hermite Spline
Values of a Discrete Signal Derivative
Optimized Structure of Farrow Filter on the Basis of Hermite Splines
Conclusions
References
Using Farrow Filter of Signal Digital Resampling on the Basis of Spline Interpolation
Introduction
Recalculating Indexes of Input Signal Samples in case of Piecewise and Cubic Spline Interpolation
Using Farrow Filter on the Basis of Spline Interpolation to Compensate Fractional Signal Delay
Using Farrow Filter on the Basis of Cubic Hermite Splines as a Digital Signal Interpolator
Using Farrow Filter on the Basis of Spline Interpolation for Fractional Frequency Change of Signal Sampling
Conclusions
References
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