IIR System Structure MCQ Quiz – Objective Question with Answer for IIR System Structure

From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N+1 multiplications are required.

From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N additions are required.

From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N+1 memory locations are required.

From the direct form-II realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then Max[M, N] memory locations are required.

A signal flow graph provides an alternative, but an equivalent graphical representation to a block diagram structure that we have been using to illustrate various system realizations. The basic elements of a flow graph are branches and nodes.

The equivalent filter structure of the given signal flow graph in the direct form-II is given as
Thus from the above structure, the system has two zeros and two poles.

The summing node is the node that is used in the signal flow graph which replaces the adder in the structure of a filter.

The input to a system originates at a source node and the output signal is extracted at a sink node.

According to the transposition or flow-graph reversal theorem, if we reverse the directions of all branch transmittances and interchange the input and output in the flow graph, then the system remains unchanged. The resulting structure is known as transposed structure or transposed form.

The structure given in the question is the transposed direct form-II structure of a two-pole and two zero IIR systems.

From the given figure, it consists of a parallel bank of single-pole filters and thus it is called a parallel form structure.

Although the state space or the internal description of the system still involves a relationship between the input and output signals, it also involves an additional set of variables, called State variables.

The state variables provide information about all the internal signals in the system. As a result, the state-space description provides a more detailed description of the system than the input-output description.

We define the state of a system at time n0 as the amount of information that must be provided at time n0, which, together with the input signal x(n) for n≥n0 determines the output signal for n≥n0.

According to the definition of the state of a system, the system consists of two components called the memory component and memoryless component.

The transpose of the matrix F is obtained by interchanging its rows and columns, and it is denoted by FT. The system thus obtained is known as Transposed system.

If h(n) is the impulse response of the single input single output system, and h1(n) is the impulse response of the transposed system, then we know that h(n)=h1>(n). Thus, a single input single output system and its transpose have identical impulse responses and hence the same input-output relationship.

A closed-form solution of the state space equations is easily obtained when the system matrix F is diagonal. Hence, by finding a matrix P so that F1=PFP-1 is diagonal, the solution of the state equations is simplified considerably.

A number λ is an Eigenvalue of F and a nonzero vector U is the associated Eigenvector if
FU=λU
Thus, we obtain (F-λI)U=0.

We know that (F-λI)U=0
The above equation has a nonzero solution U if the matrix F-λI is singular, which is the case if the determinant of (F-λI) is zero. That is, |F-λI|=0.

This determinant yields the characteristic polynomial of the matrix F.

The parallel form realization is also known as normal form representation, because the matrix F is diagonal, and hence the state variables are uncoupled.

(101.01)2=1*22+0*21+1*20+0*2-1+1*2-2=(5.25)10
=>x=5.25.

A real number X can be represented as X=\(\sum_{i=-A}^B b_i r^{-i}\) where bi represents the digit, ‘r’ is the radix or base, A is the number of integer digits, and B is the number of fractional digits.

The binary point between the digits b0 and b1 does not exist physically in the computer. Simply, the logic circuits of the computer are designed such that the computations result in numbers that correspond to the assumed location of this point.

A fixed point representation of numbers allows us to cover a range of numbers, say, x_max-x_min with a resolution

Δ=(x_max-x_min)/(m-1)

where m=2b is the number of levels and ‘b’ is the number of bits.

We can represent 5 as
5=0.625*8=0.625*23
The above number can be represented in binary float point representation as 0.101000*2011
Thus Mantissa=0.101000, Exponent=011.