# Signal Processing

• One of the broadest fields in mathematics and engineering is signal processing. Whether the signals are analog or digital, image or video, human voice or music, signal processing is concerned with methods and algorithms for analysis and synthesis, representation, and sensing and modeling of those signals. A signal is, in fact, any physical or symbolic carrier of the information. For instance, a human voice is an example of an analog signal, since our words are transferred to a person we talk to in the form of sound waves (audio signal). Conversely, a message from one computer to the other is delivered in bits, and consists of long arrays of 1’s and 0’s designed in a specific way, which constitute a digital signal. The knowledge and skills of signal processing are of importance in both academia and industry, especially in the closely related fields of machine learning, data compression, communication engineering, time series analysis, medical imaging, automatic control, etc.

Signal processing is frequently a part of academic education for applied mathematics, various engineering fields, and sound and graphic design. Courses in signal processing usually cover most of these standard topics:

• Signal sampling and reconstruction, Nyquist–Shannon sampling theorem
• Quantization and compression techniques
• Fourier analysis: Fourier transform (FT), discrete Fourier transform (DFT), short-time Fourier transform (STFT)
• Wavelet transform
• Laplace and z-transform
• Linear time-invariant theory
• Continuous-time and discrete-time systems
• Transfer functions
• Digital filters: finite impulse response (FIR) and infinite impulse response (IIR) filters
• Multirate digital signal processing (interpolation, decimation and oversampling)
• 2D Fourier transform
• Fast Fourier transform (FFT) algorithms
• Analog-to-digital and digital-to-analog conversion (AD/DA conversion)
• Power spectrum estimation
• Noise reduction
• Signal processing applications

The tutors in our math department are specialized to help in any of the mentioned subtopics, as their educational background is from such fields as applied mathematics, electrical engineering, or computer science. Whether you have an assignment which requires an underlying knowledge of probabilistic theory, linear algebra and calculus, or whether you have a more practical task to implement a theoretical model in appropriate programming language and development environment (C/C++, MATLAB, Python, R, SPSS, Eclipse, etc.), we can assist you. Some of the topics in which we tutor range from the fundamental time-frequency manipulations, such as convolution, windowing and Fourier transform, to the more advanced applications such as adaptive filtering, ARMA modelling, or parametric spectral estimations with ESPRIT and MUSIC algorithms.

The applications in which signal processing is crucial are vast and ever increasing. Let’s just take a simple phone call for example, whether using mobile telephony or a Voice over IP (VoIP) application such as Skype or WhatsApp. On the sender’s side, it first requires analog-to-digital (AD) conversion of speech, coding the signal according to GSM standards, and employing cancellation of the surrounding noise. On the receiver’s side, the signal is decoded and converted from digital back to analog signal (DA conversion) and the sound is produced using filters. The numerous jpeg images, MP3 songs and MP4 clips stored on our phones, are typical examples of audio, image and video compression, respectively. Signal processing is also applicable to remote sensing, ranging across various body scanners (CAT, MRI, airport security check), volcano and seismic activity analysis, and consumer electronics (hearing aids, echo and previously mentioned noise cancellation).

In addition to any course books you may have, the Internet is rich in resources on signal processing. Whether you prefer online lectures or spreadsheets with problems and solutions, or maybe just want to follow the latest topics in the field, here are some places to begin looking:

Open course from École Polytechnique Fédérale de Lausanne (EPFL): https://www.coursera.org/learn/dsp

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