# Digital Signal Processing and Linear Algebra

To add on this, the use of linear algebra is focused in description of algorithms used in in solving tensors and structured matrices.

In recent times, discrete data (digital) data is preferred in data transmission as compared to continuous data in computers to solve various engineering problems. The use of difference equations is accompanied by numerical solution that is as a result of combination of related difference equation. One important application of difference equation is in the discrete time-signals. Here, the definition of functions is only on integers and then visualized as number sequence.

Linear signal transmission is a form of digital signal processing. Eigen value distribution is used in relating matrices in terms of frequency – selective channels and capacity of frequency flat in linear signal transmission. These are used in the linear precoding scheme. Linear precoding simply refers to linear transformation of signals. In linear precoding, the information used to carry bit sequence blocks is mapped onto signal sequence with transformational matrix. Using this scheme, a redundancy is introduced in the data to be transmitted before transmission. In cases where there arises some errors in the transmission, there is introduction of error correction codes to correct the erroneous bits. The use of linear precoding is essential in OFDM, Discrete multi-tone, Coded OFDM, among others. Moreover, linear precoding is used in the enhancement of the ergodic capacity within a given channel by altering the Eigen structure of the chosen channel, and in this, there is application of linear transmission.

An example of application of digital signal processing is seen in image compression. There are various methods that are utilized in image compression. The basic and most common way of signal processing is singular value decomposition method. Image compression is applied main to save costs, memory