This course focuses on the fundamentals of digital signal processing that covers the fundamentals of signals, systems and transforms.

Octave.tar.gz

octave-codewidget

octave-jupyter

We live in a world filled with signals which can be represented by sequences of numbers in a digital machine. These sequences of numbers can be manipulated by algorithms and have numerous applications in audio, images, video, wireless transmission and countless other domains. 

In this course, you’ll understand the field of digital signal processing with a focus on the design and analysis of signals, and algorithms. You’ll cover the DSP fundamentals of signals, systems and transforms. You’lll learn about the basic signal types and perform different operations. You’ll develop an understanding about the frequency domain and how to represent signals in time, and the transformation from one domain to the other using the Fourier transform. You’ll also learn about digital systems. Finally, you’ll develop a practical OFDM system focusing on modulation and demodulation.

By the end of this course, you’ll be able to model, analyze and design signals and systems in greater depth, in the time and frequency domains.

Fundamentals of Digital Signal Processing

The real part is even, and the imaginary part is odd.

The real part is even, and the imaginary part is zero.

The real part is odd, and the imaginary part is even.

The real part is zero, and the imaginary part is even.

Construct a real and even signal in Python and compute its DFT. Now plot the real and imaginary parts of this DFT. What do you observe?

Construct a real and even signal in Python and compute its DFT. Now plot the real and imaginary parts of this DFT. What do you observe?

The real part is odd, and the imaginary part is zero.

The real part is zero, and the imaginary part is odd.

Construct a real and odd signal in Python and compute its DFT. Now plot the real and imaginary parts of this DFT. What do you observe?

Construct a real and odd signal in Python and compute its DFT. Now plot the real and imaginary parts of this DFT. What do you observe?

If $\cos \omega t$ is the reference with a phase at $0^\circ$, what would be the phase of $\sin\omega t$?

If <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>cos</mi><mo>⁡</mo><mi>ω</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">\cos \omega t</annotation></semantics></math>cosωt is the reference with a phase at <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>0</mn><mo>∘</mo></msup></mrow><annotation encoding="application/x-tex">0^\circ</annotation></semantics></math>0∘, what would be the phase of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sin</mi><mo>⁡</mo><mi>ω</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">\sin\omega t</annotation></semantics></math>sinωt?

A $100$ kHz sinusoidal signal is time shifted by $1~\mu s$. What is the phase shift of this signal?

A <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>100</mn></mrow><annotation encoding="application/x-tex">100</annotation></semantics></math>100 kHz sinusoidal signal is time shifted by <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mi>μ</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">1~\mu s</annotation></semantics></math>1 μs. What is the phase shift of this signal?

If we sum the squared absolute values in a signal, the answer is $96$. What is the sum of squared absolute values in the 1024-point DFT of this signal?

If we sum the squared absolute values in a signal, the answer is <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>96</mn></mrow><annotation encoding="application/x-tex">96</annotation></semantics></math>96. What is the sum of squared absolute values in the 1024-point DFT of this signal?

Test your knowledge about Fourier transform properties through this quiz.

Introduction to Signals

Basic Signals and Operations

Complex Signals and the Frequency Domain

Sampling a Signal

The Discrete Fourier Transform

Fourier Transform Properties

Digital Systems

Putting It All Together: An OFDM Modem

Demodulating an OFDM Signal Stream

The Last Words

Bibliography

Quiz 4