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Digital Filter Structure
The difference equation
If bk= 0 non recursive or all zero filter.
Direct Form – I
1. Easily implemented using computer program.
2. Does not make most efficient use of memory = M+Np+NF delay elements.
Direct form-II
Smaller no. of delay elements = Max of (M, Np) + NF
Disadvantages of D-I & D-II
1. They lack hardware flexibility, in that, filters of different orders, having different no. of multipliers and delay elements.
2. Sensitivity of co-efficient to quantization effects that occur when using finite -precision
arithmetic.
Cascade Combination of second-order section (CSOS)
Ex:
Ex:
Parallel Combination of Second Order Section (PSOS)
Ex:
Ex:
obtain PSOS
A = 8/3 B = 10 C = -35/3
Jury – Stability Criterion
| ROWS | COEFFICIENTS |
1 2 | bo b1 ……. bN bN bN-1 ……. bo |
3 4 | Co C1 ……. CN-1 CN-1 CN-2 ……. Co |
5 6 | do d1 ……. dN-2 dN-2 dN-3 ……. do |
. . . 2 N-3 | r0 r1 r2 |
i. D(1) > 0
ii. (-1)N D(-1) > 0
Ex:
1 2 | 4 3 2 1 1 1 1 2 3 4 |
3 4 | 15 11 6 1 1 6 11 15 |
| 5 | 224 159 79 |
D(1) = 4+3+2+1+1 = 11 > 0, (-1)4 D(-1) = 3 >0
Stable.
Ans: Unstable
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FAQs on Digital Filter Structure - Signals and Systems - Electronics and Communication Engineering (ECE)
| 1. What is a digital filter? |  |
Ans. A digital filter is a system that processes a digital signal to modify or enhance certain aspects of the signal. It is typically implemented using mathematical algorithms and operates on discrete-time samples of the signal.
| 2. What are the advantages of using a digital filter over an analog filter? | |
Ans. There are several advantages of using a digital filter over an analog filter. Firstly, digital filters offer greater flexibility and can be easily adjusted or reconfigured to meet different requirements. Secondly, digital filters can be implemented using software, making them more cost-effective and easier to replicate. Additionally, digital filters are less prone to noise and distortion compared to analog filters.
| 3. What are the different types of digital filter structures? | |
Ans. There are various types of digital filter structures, including Finite Impulse Response (FIR) filters and Infinite Impulse Response (IIR) filters. FIR filters have a linear phase response and are generally more stable, while IIR filters can achieve a sharper frequency response but may be more susceptible to instability.
| 4. How do I choose the appropriate digital filter structure for my application? | |
Ans. The choice of digital filter structure depends on the specific requirements of your application. If you need a filter with a linear phase response, a FIR filter would be suitable. On the other hand, if you require a sharper frequency response or have limited computational resources, an IIR filter may be preferred. It is important to consider factors such as filter order, passband ripple, stopband attenuation, and computational complexity when selecting the appropriate digital filter structure.
| 5. Can digital filters be used for real-time signal processing? | |
Ans. Yes, digital filters can be used for real-time signal processing. By processing the discrete-time samples of a signal in real-time, digital filters can modify the signal according to the desired filtering characteristics. This makes them suitable for a wide range of applications, including audio processing, image filtering, and telecommunications. However, it is important to ensure that the computational requirements of the digital filter can be met in real-time to avoid any delays or latency issues.
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