Digital Signal Processing

In summary, FIR systems do not necessarily have to be causal, but they are if they operate in real time. Causal systems have outputs that only depend on present and prior inputs and outputs, while non-causal systems have outputs that depend on future inputs. FIR systems' outputs only depend on the input, while IIR systems' outputs also depend on prior outputs. The presence of output terms in the right hand side of a difference equation indicates that the system is IIR. In terms of transfer functions, IIR systems will have a denominator polynomial, while FIR systems will only have a numerator polynomial. The example h(n) = 5^n . U(-n) is not a typical FIR or IIR system.
  • #1
cf9219
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I have a couple of questions about the theory about how to tell whether a system is casual and FIR or IIR.

First point is about a casual system. Is it true that all FIR systems are casual? How can you tell if an IIR system is casual?

I am I correct in thinking that a FIR system only has a numerator and IIR system has both a numerator and denominator?

For example: h(n) = u(n+1) -u(n-1) and h(n) = 5^n . U(-n)

Are both of these FIR systems?
 
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  • #2
cf9219
Not all FIR systems are causal. (If they operate in real time they must be causal).
Causal means that the present output depends only on the present and prior inputs and outputs. Non-causal means the output depends on future inputs. Your example h(n) = u(n+1) -u(n-1) is non-causal because the output at time n depends on the input at time n+1.

A FIR system's output depend only on the input (and its delayed copies). An IIRs output depends on prior outputs as well, in other words there is feedback. If the right hand side of your difference equation contains output terms, it is IIR. Your example h(n) = u(n+1) -u(n-1) is FIR since no "h" terms appear in right hand side.

You are right about the transfer functions. When we transform your difference equations into the z-domain, IIR filters will have a denominator polynomial (and potentially a numerator polynomial).

Finally, your second example: h(n) = 5^n . U(-n) seems strange.
 
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1. What is Digital Signal Processing (DSP)?

DSP is the manipulation and analysis of digital signals using mathematical algorithms. It is used to improve the quality of signals, extract information from them, and compress data for efficient storage and transmission.

2. What are some applications of DSP?

DSP is used in a wide range of fields such as audio and video processing, telecommunications, medical imaging, and radar and sonar systems. It is also used in consumer electronics like smartphones, digital cameras, and home theater systems.

3. How does DSP differ from analog signal processing?

DSP operates on digital signals, which are represented by discrete values, while analog signal processing deals with continuous signals. DSP offers more flexibility, accuracy, and cost-effectiveness compared to analog signal processing.

4. What are some common techniques used in DSP?

Some common techniques used in DSP include filtering, convolution, Fourier analysis, and digital modulation. These techniques are used to remove noise, extract desired information, and manipulate signals for specific purposes.

5. What are the benefits of using DSP?

DSP allows for more precise control and manipulation of signals compared to analog processing. It also offers the ability to store and transmit signals in a more efficient manner. Additionally, DSP allows for the integration of multiple functions into a single device, reducing the need for separate hardware components.

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