Analog signal processing operations cannot be done very precisely either since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

The anti aliasing filter is an analog filter which has a twofold purpose. First, it ensures that the bandwidth of the signal to be sampled is limited to the desired frequency range. Using an antialiasing filter is to limit the additive noise spectrum and other interference, which often corrupts the desired signal. Usually, additive noise is wideband and exceeds the bandwidth of the desired signal.

The in-band quantization noise variance is given as: \\(\\sigma_n^2=\\int_{-B}^B |H_n (F)|^2 S_e (F)dF\\) where \\(S_e (F)=\\frac{\\sigma_e^2}{F_(s)}\\) is the power spectral density of the quantization noise.

The anti-aliasing filter is an analog filter which has a twofold purpose.

In DM, Furthermore, the two integrators at the encoder can be replaced by a single integrator placed before the comparator. This system is known as sigma-delta modulation (SDM).

\\(D_q (z)=\\frac{H(z)}{1+H(z)} X(z)+\\frac{1}{1+H(z)} E(z)\\)

The integrator is modeled by the discrete time system with system function

Once the desired frequency band is selected we can specify the sampling rate and the characteristics of the pre filter, which is also called an anti aliasing filter. The anti aliasing filter is an analog filter which has a twofold purpose.

Once we have specified the pre filter requirements and have selected the desired sampling rate, we can proceed with the design of the digital signal processing operations to be performed on the discrete-time signal. The selection of the sampling rate Fs=1/T, where T is the sampling interval, not only determines the highest frequency (Fs/2) that is preserved in the analog signal but also serves as a scale factor that influences the design specifications for digital filters and any other discrete-time systems through which the signal is processed.

The performance of the SDM system is therefore determined by the noise system function H_(n)(z), which has a magnitude frequency response: \\(|H_n (z)|=2 |sin⁡ \\frac{πF}{F_s}|\\).