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# Introduction

This page describes how to infer the variable precision digital signal processing (DSP) blocks in Stratix® V devices to build complex multipliers in FFT applications.

http://www.altera.com/literature/wp/wp-01140-fir-fft-dsp.pdf

This page contains the following complex multipliers to demonstrate Stratix V DSP Block capabilities:

• 18x18 complex multiplier

• 18x25 cpmplex multiplier

• 27x27 complex multiplier

# 18x18 complex multiplier

Using the dual 18x18 multipliers in a single DSP block allows a designer to implement an 18x18 bit complex multiply using only two DSP blocks, as shown in Figure 1

18x18 complex multiply

(x+j*y)*(cos+j*sin) = (x*cos-y*sin)+j*(x*sin+y*cos)

# 18x25 complex multiplier

For 18-bit twiddle factor with 25-bit data, the complex mulplication can be rearranged as in Eq.1

(x+j*y)*(cos+j*sin) = (x*cos-y*sin) + j*(x*sin+y*cos)

= ((x-y)*cos + (cos-sin)*y) + j*((x+y)*sin + (cos-sin)*y)

By using the 26-bit pre-adder and a 27-bit x 27-bit multiplier available in Stratix V DSP block, the 18x25 complex multiplication can be structured as shown in Figure 3.

# 5/5a/Dsp_block5_fft_figure3.JPG ( Dsp block5 fft figure3.JPG - click here to view image )

Structured this way, an 18x25 complex multiply operation takes only three variable precision blocks.

# 27x27 complex multiplier

Using the dual 18x18 multipliers in a single DSP block allows a designer to implement an 18x18 bit complex multiply using only two DSP blocks, as shown in Figure ?

27x27 complex multiply

(x+j*y)*(cos+j*sin) = (x*cos-y*sin)+j*(x*sin+y*cos)

# 5/51/Dsp_block5_fft_figure6.JPG ( Dsp block5 fft figure6.JPG - click here to view image )

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