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I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration

For example, let assume the filter is fed a constant input of magnitude C. What would be the best method to calculate the internal state variables as the filter approaches steady state?

When I run a simulation, it appears that S1 and S2 are negatives of one another (S1 = -S2). Is there a way to calculate the exact values?

My best guess is that I need to set-up a system of equations and then find the steady-state output (given constant input C). However, my calculations seem to fall apart when I actually try to doing them.

Edit: So after working this problem a little longer, I was able to determine the following:

$$ S_{1}[n] = -S_{2}[n] = X[n]\cdot (Gain_{DC} - b_{0}) $$$$ S_{1}[n] = X[n]\cdot (Gain_{DC} - b_{0}) $$

The DC gain is then found by taking the Z transform of difference equations and setting Z = 1.

However, I'm still not sure why S1 = -S2. Maybe someone can comment on this.

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration

For example, let assume the filter is fed a constant input of magnitude C. What would be the best method to calculate the internal state variables as the filter approaches steady state?

When I run a simulation, it appears that S1 and S2 are negatives of one another (S1 = -S2). Is there a way to calculate the exact values?

My best guess is that I need to set-up a system of equations and then find the steady-state output (given constant input C). However, my calculations seem to fall apart when I actually try to doing them.

Edit: So after working this problem a little longer, I was able to determine the following:

$$ S_{1}[n] = -S_{2}[n] = X[n]\cdot (Gain_{DC} - b_{0}) $$

The DC gain is then found by taking the Z transform of difference equations and setting Z = 1.

However, I'm still not sure why S1 = -S2. Maybe someone can comment on this.

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration

For example, let assume the filter is fed a constant input of magnitude C. What would be the best method to calculate the internal state variables as the filter approaches steady state?

When I run a simulation, it appears that S1 and S2 are negatives of one another (S1 = -S2). Is there a way to calculate the exact values?

My best guess is that I need to set-up a system of equations and then find the steady-state output (given constant input C). However, my calculations seem to fall apart when I actually try to doing them.

Edit: So after working this problem a little longer, I was able to determine the following:

$$ S_{1}[n] = X[n]\cdot (Gain_{DC} - b_{0}) $$

The DC gain is then found by taking the Z transform of difference equations and setting Z = 1.

2 added 339 characters in body
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I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration

For example, let assume the filter is fed a constant input of magnitude C. What would be the best method to calculate the internal state variables as the filter approaches steady state?

When I run a simulation, it appears that S1 and S2 are negatives of one another (S1 = -S2). Is there a way to calculate the exact values?

My best guess is that I need to set-up a system of equations and then find the steady-state output (given constant input C). However, my calculations seem to fall apart when I actually try to doing them.

Edit: So after working this problem a little longer, I was able to determine the following:

$$ S_{1}[n] = -S_{2}[n] = X[n]\cdot (Gain_{DC} - b_{0}) $$

The DC gain is then found by taking the Z transform of difference equations and setting Z = 1.

However, I'm still not sure why S1 = -S2. Maybe someone can comment on this.

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration

For example, let assume the filter is fed a constant input of magnitude C. What would be the best method to calculate the internal state variables as the filter approaches steady state?

When I run a simulation, it appears that S1 and S2 are negatives of one another (S1 = -S2). Is there a way to calculate the exact values?

My best guess is that I need to set-up a system of equations and then find the steady-state output (given constant input C). However, my calculations seem to fall apart when I actually try to doing them.

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration

For example, let assume the filter is fed a constant input of magnitude C. What would be the best method to calculate the internal state variables as the filter approaches steady state?

When I run a simulation, it appears that S1 and S2 are negatives of one another (S1 = -S2). Is there a way to calculate the exact values?

My best guess is that I need to set-up a system of equations and then find the steady-state output (given constant input C). However, my calculations seem to fall apart when I actually try to doing them.

Edit: So after working this problem a little longer, I was able to determine the following:

$$ S_{1}[n] = -S_{2}[n] = X[n]\cdot (Gain_{DC} - b_{0}) $$

The DC gain is then found by taking the Z transform of difference equations and setting Z = 1.

However, I'm still not sure why S1 = -S2. Maybe someone can comment on this.

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How would I calculate the state-variables of digital biquad filter (direct form II transposed) at steady-state?

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration

For example, let assume the filter is fed a constant input of magnitude C. What would be the best method to calculate the internal state variables as the filter approaches steady state?

When I run a simulation, it appears that S1 and S2 are negatives of one another (S1 = -S2). Is there a way to calculate the exact values?

My best guess is that I need to set-up a system of equations and then find the steady-state output (given constant input C). However, my calculations seem to fall apart when I actually try to doing them.