How we fixed our Ikea wardrobe after the bar fell

Our apartment has no bedroom closet space. There are two coat closets and a linen closet all clustered in the same wall between the living room and office and near the bathroom, but there is no storage in the bedroom. So a while back, we bought three large Ikea wardrobes that fit nicely next to each other down one of the walls of our bedroom. This particular wardrobe model was one of Ikea's budget options (i.e., it was not one of their crazy customizable types; it basically came as a complete unit). The closet bar (shown here without the shelf that is usually above it) should attach to the closet using a plastic insert like this (click on the image for a larger and clearer version):

As you may be able to see, there is a large vertical scrape a few inches beneath the plastic insert. That scrape came into our lives when the plastic insert on the left side of the bar failed ("wardrobe malfunction"), which sent the awkward-shaped metal closet bar (and the clothes hanging on it) into the floor of the wardrobe. As you can see, there is a cantilever-type support jutting out from the plastic insert that sheared off (pretty clean cut, actually):

Ikea often keeps spare parts like this on hand that you can grab for free in bins from the store, but we didn't want to drive all the way to West Chester to look for them, and we were pretty sure these wardrobes were discontinued and these (likely specialized) parts were not available. So we went to Meijer instead (it was too late to go to a hardware store to find real closet accessories) to look for a way to hack together a good pre-fabricated furniture fix.

Just before we were about to give up, we found these corner braces that looked like the perfect size and shape for our problem. They were about $2.50 for a pack of 2 (in case any of the other supports ever break later).

So here's how we used a corner brace to support the closet bar:

As a bonus, the screws that came with the corner brace were short enough to not protrude out the side of the wardrobe. They were self-tapping screws, but I didn't trust them in the Ikea-style formica-covered particle board, and so I pre-drilled some small holes first, and that worked pretty well. We used a zip tie to fix the bar vertically; however, we also experimented with binder rings that we had stowed away in our office supplies. The binder rings actually provided a much tighter fit so that the bar didn't wiggle at all; however, as strange as it sounds, the zip ties were a little more discrete as they hugged the corner brace snugly.

[ I should note that I took off the shelf to get easier access to the closet. That meant pulling out the three small brads/nails attaching the masonite-ish backing. Because the area moment of inertia of that backing is very high, I think it provides significant support to the closet structure as a whole. So afterward, I pulled the closet out and put the nails back in a different spot. I probably could have left the shelf in through the whole fix. ]

I almost like the look of our fix better than the Ikea insert (which looks like it has a tenuous hold on the bar anyway).

[ You can also find this post at Jessie and Ted's blog. ]

Well, I have a Google+ account now...

UPDATE: Yes, it does appear like I have invitations to give out. Yes, if you e-mail me, I'll do my best to send you one.

You can my Google+ profile at:

http://profiles.google.com/ted.pavlic

Overall, initial reactions are good. There are some bugs to fix and some things to clean up, but I think I'd "+1" it.

Someone asked me about Hilbert transforming minimum-phase magnitude responses today...

Someone sent me this e-mail today:

Thank you for contributing to the Wikipedia article about minimum phase. I gather from the article that I should be able to use the Hilbert transform to compute a phase response from the amplitude response of a minimum phase system. Yet when I compute (in Matlab) the Hilbert transform of the log of the amplitude response of a Butterworth filter (sampled at uniform frequency intervals), the result is not real and does not resemble the phase response of a Butterworth at all. I expected that it would equal the phase response of a Butterworth since a Butterworth is minimum phase. What have I missed? Thank you.

So I responded in an e-mail, and I've pasted that e-mail here.

Assuming that you are using a high-order filter, are you unwrapping your phase? See the MATLAB function "unwrap" for details. Another easy fix is to ensure you're using the NATURAL log to extract the exponent of the magnitude as an exponential. In MATLAB, "log" is natural log and "log10" is common log.

If you still have the problem, make sure your filter is truly minimum
phase. In particular, the transfer function and its inverse must be
stable and CAUSAL. The causality condition is redundant so long as your
notion of stability includes poles induced from unmatched zeros. For
example, the discrete-time filter:

z + 0.5

is not causal and thus has a pole at infinity. So it does not meet the criteria for being minimum phase. On the other hand, the filter:

(z+0.5)/z

is minimum phase. So let's take its impulse response. In MATLAB, you could try:

h = impulse(tf( [1,0.5], [1,0], 0.1));

or...

z = tf('z');
h=impulse( (z+0.5)/z );

or just read it from the numerator and add as many zeros as you'd like...

h=[1,0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];

Then use the FFT:

H=fft(h);

Then use the discrete-time Hilbert transform of the NATURAL log:

X=hilbert(log(abs(H)));

Then, to compare, use "plot":

plot( 1:length(h), -imag(X)*180/pi, 'o', ...
      1:length(h), angle(H)*180/pi, 'x' )

I think you'll find that each x is circled.

To summarize:

h=[1,0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
H=fft(h);
X=hilbert(log(abs(H)));
plot( 1:length(h), -imag(X)*180/pi, 'o', ...
      1:length(h), angle(H)*180/pi, 'x' )

Here's another interesting case that won't match as well because of the discrete-time approximation.

z = tf('z',1);
H = (z + 0.5)/(z);
[mag,phase,w]=bode(H);
mag=mag(:); phase=phase(:); w=w(:);
X=hilbert(log(mag));
plot(w/pi,-imag(X)*180/pi,w/pi,phase)

As you can see, these two match pretty well in the interior region. You can make some interesting observations about the edges where they don't match well.