FFT (Fast Fourier Transform)

The delay corrected signal from each channel is then Fourier transformed in real-time. The functions of FFT card can be broadly classified in the following :

• Fringe stopping : As the earth rotates, each antenna experiences different radial velocities with respect to the source. Hence, the signal at each antenna is Doppler shifted in frequency by different amounts depending on the position of the antenna in the array. This effect is corrected.

• Data Windowing : At the first stage of FFT pipeline fringe stopped data is multiplied by desired window function (512 independent sample) having applications in controlling the side-lobe level of FFT.

• FFT : A 512 point FFT is achieved (one every $\approx 16 \mu s$) by using a pipeline of 5 ASICs that can perform Radix-2 and Radix-4 FFT butterfly after suitable twiddling operation of 32 MHz rate. This gives a continuous stream of 256 complex spectral channels.

• FSTC : Fractional sampler time corrections (i.e. delay corrections that are fraction of the sampling interval) are achieved by multiplying the complex spectra output of the FFT pipeline by the relevant phase gradients. Strictly speaking this is achieved by adding suitable phase to the final stage twiddle phase ( $\theta_{nTWID}$) just before the last radix-2 operation.