Error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated and, in the event the check values do not match, corrective action can be taken against data corruption( Wikipedia )
Convolution between two sounds ( University project ) The first part of thr code consists of the colvolution between two vectots ( vector A is given by the user, and vector B is standard [ 1/5, 1/5, 1/5, 1/5, 1/5].
The second part, which is the most interesting one, involves the convolution between two sound. Firstly, the sounds need to be converted to vectors. The WavFileToArray uss python functions(numpy) and turns the wav files into vectors. After the convolution is done,the ArrayToWavFile, does the reverse process and turns the final vector into a wav file.
The last part, creates a white sound and then performs the same convolution methos as is the previous two parts.
MyConvolve function: This is the function that is included in every part of the script since it's the once that convolutes the two given vectors each time. The code is based on the following formula : image ( pic from wikipedia )
The exchange rate is a single-bit error detection method, in which a ninth bit, the exchange rate bit, is added to the end of each row of 8 bits.The value of the extra bit is used to detect odd errors within the group of 8 bits.This is divided into odd and even (here we consider the case of even). The procedure followed is as follows: We count the number of bits that have a value of "1". If we are in the first case and the number of "1" is odd then we accept the message otherwise we request retransmission. Similarly in the other case for an even number of units."
1.1 The first part being responsible for even parity, checks whether the number of units is odd or even. If it is odd it adds one unit to the end of the message and if it is even it adds a zero.
1.2 The following code section is responsible for error detection and considers three different cases. 1.There is no error 2.There is one error 3.There are two errors
We notice that in the case of two errors it tells us that it accepts the message this is because by toggling the two bits the "balance" between 0 and 1 is restored and the error is not detected.
1.3 In this case we follow a 2-dimentional exchange rate, the logic is applied is similar to the one earlier but instead of having one single line, the bits are divided equally into 4 lines.
1.4 Following the same logic we did in 1.2, we notice that the 'network' is able to catch the errors.
NOTE(not in the code): Are there any error patterns that are not detected in two-dimensional parity, and if so which ones?In the case where there is a double toggle in one column and one row then the algorithm will not be able to detect the error due to the "balance" as mentioned in question 1.2.For a better understanding the following example is given.
