Discrete systems in series and parallel

Discrete systems in series Let as say that we have two discrete systems and their impulse responses are h1(n) and h2(n). Then when these discrete systems are connected in series, then overall impulse response: Where: As you noticed there were changing made: This is nothing more than convolution of impulse responses of both discrete systems: Discrete systems in parallel If we have two discrete systems connected in parallel: As we see there is simple sum of output queues of each discrete system. So we can assume, that overall impulse response is as sum of systems connected in parallel:

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Impulse Response of discrete system

Impulse signal can be represented as: d[n] = 1, if n=0 d[n] = 0, otherwise it can also be written like d=[1,0,0,0,…] Impulse Response The impulse response h(n) is the response of filter L() at time n to unit impulse occurring at time 0. h(n)=L(d(n)) Lets see how discrete system can be described when impulse response is known We know that: In the linear system this can be written as follows: Because h(n-k)=L(d(n-k)) Then: What do we get? There is obvious, that linear system can be described by its impulse response. The last expression is called convolution. This is the heart of DSP Filtering. To write this sum in more convenient matter is assumed that: Matlab example Matlab example: % Plot an unit impulse signal n = -7:7; x = [0 0 0 0 0 0 0 1 2 3 0 0 0 0 0]; subplot(4,2,1); stem(n, x); limit=[min(n), max(n),…

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What is a linear system?

Discrete system is nothing more than algorithm, where input is transformed to output. The output is transformed by operator L() which describes discrete system. Lets see few most common operators of discrete systems. Delay This means that output queue is delayed by on sample. Multiplication This operator takes each sample of input queue and multiplies by constant a. Sum operator Takes two or more sample queues and adds them in the output. Assuming we can say, that the system is linear if input sum reaction is equal to sum of inputs reactions: The system has stable parameters if: y(n-k)=L(x(n-k)), this means that output delay should be the same as input. It is obvious that delay, multiply and sum operators are linear and has stable parameters. We will need then for further lessons.

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Understanding of discrete signals

Discrete signals can be generated by software or obtained from real world through ADC. Discrete signals are sampled from analog signals. So you get samples in fixed time intervals. Discrete signal is as sequence of numbers. The element number n of sequence is marked as x(n). The most common number rows: Unit sample sequence d[n] = 1, if n=0 d[n] = 0, otherwise You can describe it in Matlab like % Plot an unit impulse signal n = -5:5; x = 0*n; index=find(n==0); x(index)=1; % plot stem(n, x); axis([-inf, inf, -0.2, 1.2]); xlabel(‘n’); ylabel(‘x’); title(‘Unit Impulse Signal delta[n]’); Unit Step Sequence u[n] = 1, if n>=0 u[n] = 0, otherwise You can describe it in Matlab like: % Plot an unit impulse signal n = -5:5; x = 0*n; index=find(n>=0); x(index)=1; % plot stem(n, x); axis([-inf, inf, -0.2, 1.2]); xlabel(‘n’); ylabel(‘x’); title(‘Unit Step Signal u[n]’); As you can see step…

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AD9288 Protel Footprint

The AD9288 is a dual 8-bit monolithic sampling analog-to-digital converter with on-chip track-and-hold circuits and is optimized for low cost, low power, small size and ease of use. The product operates at a 100 MSPS conversion rate with outstanding dynamic performance over its full operating range. Each channel can be operated independently. The ADC requires only a single 3 V (2.7 V to 3.6 V) power supply and an encode clock for full-performance operation. No external reference or driver components are required for many applications. The digital outputs are TTL/CMOS compatible and a separate output power supply pin supports interfacing with 3.3 V or 2.5 V logic. The encode input is TTL/CMOS compatible and the 8-bit digital outputs can be operated from +3 V (2.5 V to 3.6 V) supplies. User selectable options are available to offer a combination of power down modes, digital data formats and digital data timing…

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LPC229x protel library

The LPC2292 microcontrollers are based on a 16-bit/32-bit ARM7TDMI-S CPU with real-time emulation and embedded trace support, together with 256 kB of embedded high-speed flash memory. A 128-bit wide memory interface and a unique accelerator architecture enable 32-bit code execution at the maximum clock rate. For critical code size applications, the alternative 16-bit Thumb mode reduces code by more than 30 pct. with minimal performance penalty. With their 144-pin LQFP144 package, low power consumption, various 32-bit timers, 8-channel 10-bit ADC, 2/4 (LPC2292) advanced CAN channels, PWM channels and up to nine external interrupt pins these microcontrollers are particularly suitable for automotive and industrial control applications as well as medical systems and fault-tolerant maintenance buses. The number of available GPIOs ranges from 76 (with external memory) through 112 (single-chip). With a wide range of additional serial communications interfaces, they are also suited for communication gateways and protocol converters as well as…

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Emergency supply source for your electronic device

Sometimes you are needed to maintain power supply for your device for some time when the main source fails. It can be alarm system or some light source or digital clock. Of course if source interrupts are very short, there can be capacitor with big capacity connected, but it is not reliable. Better use backup battery and diode. This solution is very simple and cheap. The diode protects the back current float to battery. This doesn’t take much space to implement as the main bigger part is battery. As there just backup source it is not necessary to use rechargeable battery.

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