The DDS generates a complex sinusoid at the intermediate frequency (IF). Multiplication of the intermediate frequency with the input signal creates images centered at the sum and difference frequency (which follows from the frequency shifting properties of the Fourier transform). The lowpass filters pass the difference (i.e. baseband) frequency while rejecting the sum frequency image, resulting in a complex baseband representation of the original signal. Assuming judicious choice of IF and LPF bandwidth, the complex baseband signal is mathematically equivalent to the original signal. In its new form, it can readily be downsampled and is more convenient to many DSP algorithms.