If you are looking for a quality Postgraduate certificate that will help you specialize in one of the most promising professional fields, this is your best option” 

Advances in telecommunications are happening all the time, as this is one of the fastest evolving areas. It is therefore necessary to have IT experts who can adapt to these changes and have first-hand knowledge of the new tools and techniques that are emerging in this field. 

This Postgraduate certificate in Digital Signal Processing addresses the complete range of topics involved in this field. Its study has a clear advantage over other programs that focus on specific blocks, which prevents students from knowing the interrelation with other areas included in the multidisciplinary field of telecommunications. In addition, the teaching team of this educational program has made a careful selection of each of the topics of this program in order to offer students the most complete study opportunity possible and always linked to current events. 

This Postgraduate certificate is aimed at those interested in attaining expert knowledge of Digital Signal Processing. The main objective is for students to specialize their knowledge in simulated work environments and conditions in a rigorous and realistic manner so they can later apply it in the real world. 

Additionally, as it is a 100% online program, the student is not constrained by fixed timetables or the need to move to another physical location, but can access the contents at any time of the day, balancing their professional or personal life with their academic life. 

Don't miss the opportunity to study this Postgraduate certificate in Digital Signal Processing with TECH. It's the perfect opportunity to advance your career" 

This Postgraduate certificate in Digital Signal Processing contains the most complete and up-to-date program on the market. The most important features include: 

• The development of case studies presented by experts in Digital Signal Processing
• The graphic, schematic, and practical contents with which they are created, provide scientific and practical information on the disciplines that are essential for professional practice
• Practical exercises where self-assessment can be used to improve learning
• Special focus on innovative methodologies in Digital Signal Processing
• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments
• Content that is accessible from any fixed or portable device with an Internet connection

This Postgraduate certificate is the best investment you can make when selecting a refresher program to update your knowledge in Digital Signal Processing” 

The teaching staff includes professionals from the field of information technology, who bring their experience to this specialization program, as well as renowned specialists from leading societies and prestigious universities. 

The multimedia content, developed with the latest educational technology, will provide the professional with situated and contextual learning, i.e., a simulated environment that will provide immersive education programmed to learn in real situations. 

This program is designed around Problem-Based Learning, whereby the professional must try to solve the different professional practice situations that arise during the academic year. For this purpose, professionals will be assisted by an innovative interactive video system developed by renowned and experienced experts in Digital Signal Processing. 

This program comes with the best educational material, providing you with a contextual approach that will facilitate your learning"

This 100% online Postgraduate certificate will allow you to combine your studies with your professional work"

The structure of the contents has been designed by the best professionals in the from the engineering sector, with extensive experience and recognized prestige in the profession 

We have the most complete and up-to-date educational program on the market. We strive for excellence and for you to achieve it too" 

Module 1. Digital Signal Processing 

1.1. Introduction 

1.1.1. Meaning of “Digital Signal Processing” 
1.1.2. Comparison between DSP and ASP
1.1.3. The History of DSP
1.1.4. Applications of DSP

1.2. Discrete Time Signals 

1.2.1. Introduction 
1.2.2. Sequence Classification 

1.2.2.1. Unidimensional and Multidimensional Sequences 
1.2.2.2. Odd and Even Sequences 
1.2.2.3. Periodic and Aperiodic Sequences 
1.2.2.4. Deterministic and Random Sequences 
1.2.2.5. Energy and Power Sequences 
1.2.2.6. Real and Complex Systems 

1.2.3. Real Exponential Sequences 
1.2.4. Sinusoidal Sequences 
1.2.5. Impulse Sequence 
1.2.6. Step Sequence 
1.2.7. Random Sequence 

1.3. Discrete Time Systems

1.3.1. Introduction 
1.3.2. System Classification 

1.3.2.1. Linearity 
1.3.2.2. Invariance 
1.3.2.3. Stability
1.3.2.4. Causality 

1.3.3. Difference Equations 
1.3.4. Discrete Convolution 

1.3.4.1. Introduction 
1.3.4.2. Deduction of the Discrete Convolution Formula 
1.3.4.3. Properties 
1.3.4.4. Graphical Method for Calculating Convolution 
1.3.4.5. Justification of Convolution 

1.4. Sequences and Systems in the Frequency Domain

1.4.1. Introduction 
1.4.2. Discrete-Time Fourier Transform (DTFT) 

1.4.2.1. Definition and Justification 
1.4.2.2. Observations 
1.4.2.3. Inverse Transform (IDTFT) 
1.4.2.4. Properties of DTFT 
1.4.2.5. Examples 
1.4.2.6. DTFT Calculation in a Computer 

1.4.3. Frequency Response of a LI System in Discrete Time 

1.4.3.1. Introduction 
1.4.3.2. Frequency Response According to Impulse Response 
1.4.3.3. Frequency Response According to the Difference Equation 

1.4.4. Bandwidth Relationship - Response Time 

1.4.4.1. Duration Relationship - Signal Bandwidth 
1.4.4.2. Implication in Filters 
1.4.4.3. Implications in Spectral Analysis 

1.5. Analog Signal Sample 

1.5.1. Introduction 
1.5.2. Sampling and Aliasing 

1.5.2.1. Introduction 
1.5.2.2. Aliasing Visualization in the Time Domain 
1.5.2.3. Aliasing Visualization in the Frequency Domain 
1.5.2.4. Example of Aliasing 

1.5.3. Relationship between Analog and Digital Frequency 
1.5.4. Antialiasing Filter 
1.5.5. Simplification of the Antialiasing Filter 

1.5.5.1. Sampling Admitting Aliasing 
1.5.5.2. Oversampling 

1.5.6. Simplification of the Reconstruction Filter 
1.5.7. Quantization Noise 

1.6. Discrete Fourier Transform 

1.6.1. Definition and Foundations 
1.6.2. Inverse Transformer 
1.6.3. Examples of DFT Application and Programming 
1.6.4. Periodicity of the Sequence and its Spectrum 
1.6.5. Convolution by Means of DFT 

1.6.5.1. Introduction 
1.6.5.2. Circular Displacement 
1.6.5.3. Circular Convolution 
1.6.5.4. Frequency Domain Equivalent 
1.6.5.5. Convolution through the Frequency Domain 
1.6.5.6. Lineal Convolution through Circular Convolution 
1.6.5.7. Summary and Example of Time Calculations 

1.7. Rapid Fourier Transform 

1.7.1. Introduction 
1.7.2. Redundancy in DFT 
1.7.3. Algorithm by Decomposition in Time 

1.7.3.1. Algorithm Basis 
1.7.3.2. Algorithm Development 
1.7.3.3. Number of Complex Multiplications Required 
1.7.3.4. Observations 
1.7.3.5. Calculation Time 

1.7.4. Variants and Adaptations of the Above Algorithm 

1.8. Spectral Analysis 

1.8.1. Introduction 
1.8.2. Periodic Signals Coincident with the Sampling Window 
1.8.3. Periodic Signals Non-Coincident with the Sampling Window 

1.8.3.1. Spurious Content in the Spectrum and Use of Windows
1.8.3.2. Error Caused by the Continuous Component
1.8.3.3. Error in the Magnitude of the Non-Coincident Components
1.8.3.4. Spectral Analysis Bandwidth and Resolution 
1.8.3.5. Increasing the Length of the Sequence by Adding Zeros 
1.8.3.6. Application in a Real Signal 

1.8.4. Stationary Random Signals 

1.8.4.1. Introduction
1.8.4.2. Power Spectral Density
1.8.4.3. Periodogram 
1.8.4.4. Independence of Samples 
1.8.4.5. Feasibility of Averaging 
1.8.4.6. Scaling Factor of the Periodogram Formula 
1.8.4.7. Modified Periodogram 
1.8.4.8. Averaging with Overlap 
1.8.4.9. Welch Method
1.8.4.10. Segment Size
1.8.4.11. Implementation in MATLAB

1.8.5. Non-Stationary Random Signals 

1.8.5.1. STFT 
1.8.5.2. Graphic Representation of the STFT 
1.8.5.3. Implementation in MATLAB 
1.8.5.4. Spectral and Temporal Resolution 
1.8.5.5. Other Methods 

1.9. Design of FIR Filters 

1.9.1. Introduction 
1.9.2. Mobile Average 
1.9.3. Lineal Relationship between Phase and Frequency 
1.9.4. Lineal Phase Requirement 
1.9.5. Window Method 
1.9.6. Frequency Sample Method 
1.9.7. Optimal Method 
1.9.8. Comparison between the Previous Design Methods 

1.10. Design of IIR Filters 

1.10.1. Introduction 
1.10.2. Design of First Order IIR Filters 

1.10.2.1. Low-Pass Filters 
1.10.2.2. High-Pass Filters 

1.10.3. The Z Transform 

1.10.3.1. Definition 
1.10.3.2. Existence 
1.10.3.3. Rational Functions of Z, Zeros and Poles 
1.10.3.4. Displacements of a Sequence 
1.10.3.5. Transfer Functions 
1.10.3.6. Start of TZ Operation 

1.10.4. Bilinear Transformation 

1.10.4.1. Introduction 
1.10.4.2. Deduction and Validation of the Bilinear Transformation 

1.10.5. Design of Butterworth-Type Analog Filters 
1.10.6. Butterworth-Type IIR Low-Pass Filter Design Example 

1.10.6.1. Specifications of Digital Filters 
1.10.6.2. Transition to Analog Filter Specifications 
1.10.6.3. Design of Analog Filters 
1.10.6.4. Transformation of Ha(s) to H(z) Using TB 
1.10.6.5. Verification of Compliance with Specifications 
1.10.6.6. Digital Filter Difference Equation 

1.10.7.  Automated Design of IIR Filters 
1.10.8. Comparison between FIR Filters and IIR Filters 

1.10.8.1. Efficiency 
1.10.8.2. Stability
1.10.8.3. Sensitivity to Coefficient Quantification 
1.10.8.4. Distortion of Wave Form

This program will allow you to advance in your career comfortably"