Discrete Fourier Transform: It is very important chapter covered in DSP course. Fourier Trasnform is done to convert a signal from time domain to frequency domain. There are two types of Fourier Transform : Continuous time Fourier Transform and Discrete Time Fourier Transform. Continuous Time Fourier Transform (CTFT) is taken for continuous time signals, whereas Discrete time Fourier Transform(DTFT) is taken for discrete time signals. When We do frequency sampling of DTFT we get DFT (Discrete time Fourier Transform). Thus DFT is obtained by frequency sampling of DTFT. There are few B.Tech tuition institutes in Delhi giving tutorials for various types of Fourier Transform techniques, one of such institute is Tejas Engineers Academy located in West Delhi.
Discrete Fourier Transform is used to convert a discrete time signal from time domain to discrete frequency domain. One of the advantage of DFT is that it gives a finite number of samples in frequency domain, which can easily be stored in memory. On the other hand DTFT gives a continuous spectra which cannot be stored as samples. Disadvantage with DFT is that it requires a lot of additions and multiplications to compute the final result. There are about N2 computations done to calculate DFT. There exists an efficient algorithm to compute DFT of a sequence this algorithm is known as Fast Fourier Transform (FFT). Thus Fast Fourier Transform is used to compute DFT of a sequence with less number of additions and multiplications. There are about Nlog2N computations required to find FFT. Hence number of computations are less to find DFT using FFT. B.Tech tuition institutes in Delhi generally describes each and every details of types of FFT. There are two types of FFT techniques described by B.Tech tuition institutes in Delhi, Decimation in Time (DIT) and Decimation in Frequency (DIF).B.Tech tuition Institutes in Delhi generally provides notes for finding FFT using these techniques. Before computing FFT using DIT, sequence needs to be arranged in the order of bit reversal sequence. Bit reversal order of a sequence is obtained by first converting a sequence positions in binary form, then reading the binary sequence in reverse order for example 6 in binary is 110 when we read it in reverse order it becomes 011 which is 3, hence bit reversal value of 6 is 3. Then the bit reversal sequence is given to a signal flow graph to find the final FFT. In next post we will completely describe the procedure of finding out FFT. Many B.Tech tuition institutes in Delhi do not describe this procedure in detail to students, they tend to focus on mugging the procedure but not able to describe the details and concepts behind the procedure. Tejas Engineers Academy describes you each and every finest detail of the procedure of finding FFT.
