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Memory references in digital signal processors (DSP) are expensive due to their long latencies and high power consumption. Implementing fast Fourier transform (FFT) algorithms on DSP involves many memory references to access butterfly inputs and twiddle factors. Conventional FFT implementations require redundant memory references to load identical twiddle factors for butterflies from different stages in the FFT diagrams. In this paper, we present novel memory reference reduction methods to minimize memory references due to twiddle factors for implementing various different FFT algorithms on DSP. The proposed methods first group the butterflies with identical twiddle factors from different stages in the FFT diagrams and compute them before computing other butterflies with different twiddle factors, and then reduce the number of twiddle factor lookups by taking advantage of the properties of twiddle factors. Consequently, each twiddle factor is loaded only once and the number of memory references due to twiddle factors can be minimized. We have applied the proposed methods to implement radix-2 DIF FFT algorithm on TI TMS320C64x DSP. Experimental results show the proposed methods can achieve average of 76.4% reduction in the number of memory references, 53.5% saving of memory spaces due to twiddle factors, and average of 36.5% reduction in the number of clock cycles to compute radix-2 DIF FFT on DSP comparing to the conventional implementation. Similar performance gain is reported for implementing radix-2 DIT FFT algorithms using the new methods