# Mobile communications and digital signal processing The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing. A time-invariant filter has constant properties over time; other filters such as adaptive filters change in time. With some applications, how the phase varies with frequency can be a significant consideration.

A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain representation. They choose the domain in which to process a signal by making an informed assumption or by trying different possibilities as to which domain best represents the essential characteristics of the signal and the processing to be applied to it.

### Digital signal processing algorithms

This can be an efficient implementation and can give essentially any filter response including excellent approximations to brickwall filters. Frequency domain analysis is also called spectrum- or spectral analysis. Main article: Sampling signal processing To digitally analyze and manipulate an analog signal, it must be digitized with an analog-to-digital converter ADC. A time-invariant filter has constant properties over time; other filters such as adaptive filters change in time. It is analogous to the Laplace transform , which is used to design and analyze analog IIR filters. A filter can be represented by a block diagram , which can then be used to derive a sample processing algorithm to implement the filter with hardware instructions. A filter may also be described as a difference equation , a collection of zeros and poles or an impulse response or step response. It is then low-pass filtered and downscaled, yielding an approximation image; this image is high-pass filtered to produce the three smaller detail images, and low-pass filtered to produce the final approximation image in the upper-left. There are some commonly-used frequency domain transformations. A finite impulse response FIR filter uses only the input signals, while an infinite impulse response IIR filter uses both the input signal and previous samples of the output signal. This emphasizes the harmonic structure of the original spectrum. A causal filter uses only previous samples of the input or output signals; while a non-causal filter uses future input samples. The Fourier transform converts the time or space information to a magnitude and phase component of each frequency. With some applications, how the phase varies with frequency can be a significant consideration. The processed result might be a frequency spectrum or a set of statistics.

A finite impulse response FIR filter uses only the input signals, while an infinite impulse response IIR filter uses both the input signal and previous samples of the output signal. The Z-transform provides a tool for analyzing stability issues of digital IIR filters.

The Signal Processing for Mobile Communications Handbook provides a comprehensive survey of signal processing techniques used in mobile communications that concern the transmitter, the receiver, and the propagation channel.

Where phase is unimportant, often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared. Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. The output of a linear digital filter to any given input may be calculated by convolving the input signal with the impulse response. A filter can be represented by a block diagramwhich can then be used to derive a sample processing algorithm to implement the filter with hardware instructions.

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