TU Delft
Education Type
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2012/2013 Electrical Engineering, Mathematics and Computer Science Bachelor Computer Science and Engineering
Responsible Instructor
Name E-mail
Dr.ir. R.C. Hendriks    R.C.Hendriks@tudelft.nl
Education Period
Start Education
Exam Period
Course Language
Required for
Image processing, Imaging project
Expected prior knowledge
Analyse, lineaire algebra
Course Contents
In this course, the student learns the basic principles of signal processing. Topics that will be discussed are harmonic signals, spectral representation, Fourier transforms, sampling and aliasing, FIR and IIR filters, convolutions, linear time-invariant systems, frequency response, and spectral analysis
Study Goals
Properties of signals and Linear and time-invariant systems:
• Motivate why DSP is important for CS.
• Name the properties of signals.
• Apply a simple (FIR) linear filter to a discrete-time signal and draw
• Convert verbal description of FIR filter into its mathematical notation.
• Prove that a system is time-invariant.
• Prove that a system is linear.
• Explain the relation between the superposition principle, additivity, and
• Write down equation of impulse function.
• Decompose signal into sum of impulse functions.
• Explain why sinusoidal signals are important in DSP.

Sampling, FIR filters, and convolution:
• Applying the Shannon sampling theorem on a given signal.
• Explain the concept of aliasing, oversampling, undersampling.
• Applying zero-order and linear interpolation on given set of samples.
• Write down general FIR filter expression.
• Apply FIR filter to a discrete-time signal.
• Determine the impulse response of an FIR filter.
• Write down and explain expression of unit impulse (dirac function).
• Calculate the convolution between two sequences (signals or impulse
• Explain the properties of convolution: commutative, associative,
convolution with a (delayed) unit impulse, non-causal impulse response.

Fourier Transformations:
• Apply Euler’s and inverse Euler’s formula to functions of sinusoids.
• Explain in words the usefulness and objectives of Fourier transforms (in
terms of decomposing a signal into sinusoidal components).
• Write a periodic continuous-time signal as a sum of complex exponents,
sketch the signal in the time domain.
• From a given Fourier series of a periodic continuous-time signal sketch
the complex, amplitude, phase spectrum, and vice versa.
• Give the definition of the DTFT and DFT.
• Explain the difference between Fourier series, DTF, and DFT.
• Calculate the DTFT and/or DFT of a simple signal x[n].
• Calculate the amplitude spectrum using DTFT and/or DFT of a simple
signal x[n].
• Sketch a typical amplitude spectrum for infinite or finite length discretetime
signal x[n], and explain its axes and properties.

The frequency response:
• Explain the importance of the frequency response.
• Calculate the frequency response of an FIR filter with simple impulse response
• Sketch the magnitude and phase of a frequency response.
• Recognize and characterize the difference between a low-pass and
high-pass filter from the frequency response.
• Explain how a convolution can be calculated using the frequency
• Explain the difference between linear and circular convolution.
• Calculate the convolution result of simple signals/impulse responses by
hand using frequency responses.
• Calculated the frequency response of cascaded FIR filters.
• Explain the utility of the FFT.

IIR filters:
• Compute the output of Infinite impulse response (IIR) filters recursively.
• Determine the impulse response of first-order IIR filters.
• Determine whether first-order IIR filter is stable.
• Compute the frequency response of an IIR filter.
• Explain the influence of the filter coefficient of a first-order IIR on the frequency response.
• Be able to design simple FIR filters using the desired frequency response.

Education Method
Lectures and instructions

Book 'Signal Processing First' James H. McClellan, Ronald W. Schafer and Mark A. Yoder ISBN 0-13-120265-0 Prentice Hall.
There is a written exam at the end of the period with open questions. The students are allowed to use the list of symbols from blackboard, on which they are allowed to add additional notes. Calculators are not allowed.

During the instructions, there is the possibility to make bonus exercises, where students can earn maximum 1 extra point for the exam.