The essence of digital signal processing is a set of numerical operations, which can be implemented in software on a general-purpose digital computer or in specialized hardware. Regardless of the implementation, some of the coefficients of the digital signal processing system, the various values ​​of the signal sequence, and the results of the operations are stored in binary form in a memory cell of finite word length. If an analog signal is stored, such as a commonly used sampled signal processing system, the input analog quantity is sampled and analog-to-digital converted into a finite-length digital signal. A finite length number is a finite precision number. Therefore, in the specific implementation, it is often difficult to ensure the original design accuracy and cause errors, and even lead to erroneous results. There are mainly three factors in the digital system that cause errors due to finite word length.
First, the quantization effect produced by the analog-to-digital converter when converting an analog input signal into a digital signal
Second, the quantization effect produced when the coefficient is represented by a finite bit binary
Third, in the digital operation process, the number of bits processed for the limit digits and the finite word length effect of compressing the signal level to prevent overflow
The root cause of these errors is that the word length of the register (storage unit) is limited. The characteristics of the error are related to the type of the system, the form of the structure, the representation of the number, the way of operation, and the length of the word. On a general-purpose computer, the word length is long, the quantization step is small, and the quantization error is small. However, in dedicated hardware, such as FPGA, when implementing a digital system, the word length is short, and the finite word length effect must be considered.
What is the word length in the microcontroller?
Usually truncation is used in the FPGA, and rounding is used in the DSP (that is, rounding). So what kind of processing is the floor function and the ceil function in matlab?
Remember this indicator, which is often used in actual projects. Quick exam, do some questions!
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