ABSTRACT
This paper examined novel approach to digital signal processing of sinusoids with MATLAB using Discrete Fourier Transform. A sinusoid is a mathematical curve that describes a smooth periodic oscillation and they can be used for studies and finding possible solutions to many real life problems. In the field of Computer Engineering, it can be used for studies on sampling of digital signals, plotting of time/frequency domain of discrete signals. The study determined the effect of sampling rate on DFT. Findings reveal that an increase in sampling frequency or duration will increase the size of the DFT. Also, a time and frequency domain plot of DFT signal was implemented. It was concluded that more research should be encouraged in the area of digital signal processing, to study and solve real life problems.
- Introduction
Signals are part of our daily lives and we are surrounded by all kinds of signals in various forms. These signals are either natural or manmade. Some examples of these natural signals are speech, music, etc. Signals can be defined as any time‐varying or spatial‐varying quantity. Examples are speech or audio signal which is sound amplitude that varies in time, electronic signals, temperature readings at different hours of a day, stock price changes over days. From an engineering standpoint, signals are used for representing information. This makes signal processing very important. Signal processing operations include: capturing, enhancing, storing, and transmitting useful information. In specific terms, signals can exist in analogue and digital forms and digital signal processing involves processes for capturing analogue signals, converting them to digital signals, processing the signal, analysing the signal and producing an output. Signals can be classified as continuous or discrete. Analogue signals vary continuously in time and amplitude, and they are processed with electrical equipments containing active and passive circuit elements. Analogue signal processing (ASP) for example, radio and television receivers involve the use of electrical tools such as multipliers, logic elements and the use of special-purpose microprocessors. When analogue signals are converted into a form suitable for digital hardware, it is called a digital signal. On the other hand, a discrete signal or discrete‐time signal is a time series, sampled from a continuous‐time signal. A digital signal is a discrete‐time signal that takes on only a discrete set of Values. Digital signal processing is concerned with manipulation of signals by filtering analogue signals to get desired digital output (Taiwo and Olatayo, 2018). Digital signals are represented by binary numbers. The processing of digital signals is therefore called digital signal processing. Digitally, signals can be represented as sinusoids, which is a mathematical curve that represents a smooth periodic oscillation. A sine wave is a continuous wave. It is named after the function sine, of which it is the graph. The sine wave is important in physics because it retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property (Sienkowski, 2017). DSP functions such as sinusoid generation can be applied to solve real life problems.
To implement digital signal processing, MATLAB can be used. MATLAB is an interactive programming language that can be used in implementing DSP applications. It is a high level programming language. The package is widely used in research and industry. It is particularly well known in the following areas: meteorology, aerospace and defence; automotive; biotech, pharmaceutical; medical; and communications. Specialist toolboxes are available for a diverse range of other applications, including statistical analysis, financial modelling, image processing and so on. In this paper, MATLAB is used to implement the digital signal processing of sinusoids using Discrete Fourier Transform (DFT) – Fast Fourier Transform.
1.1 Importance of the Study
This study is important in the following ways:
- The study will help point out clearly how Discrete Fourier Transform (DFT) is applied in DSP.
- Simulation of signal sampling of sinusoids will be implemented, thereby promoting knowledge in that area of DSP.
- The study will reveal how MATLAB can be used to implement signal sampling of sinusoids using Discrete Fourier Transform (DFT).
- The study will reveal how a tine domain and frequency domain plot of DFT signal is implemented.
- One of the premiere uses of MATLAB is in the analysis of signal processing and control systems this study will provide an application of signal sampling.
- Primarily because of its advantages, DSP is now becoming a first choice in many technologies and applications hence making it very important.
- It will help stimulate interest in this area of research.
Concept of Digital Signal Processing (DSP)
Digital Signal Processing can be viewed as the analysis and manipulation of an information signal, such as audio, temperature, voice, and video with the objective of modifying or improving them in a specific way by using mathematical models such as Fourier Transform. DSP is used to work on different types of signals with the intention of filtering, measuring, or compressing. Analogue signals on the other hand differ by capturing needed information and translating it into electric pulses of varying amplitude, whereas digital signal information is translated into binary format where each bit of data is represented by two distinguishable amplitudes. Analogue signals can be represented as sine waves and digital signals are represented as square waves. DSP is applied in different fields, such as oil processing, sound reproduction, radar and sonar, medical image processing, or telecommunications. It is basically applied when signals need to be compressed and reproduced.
